Dice Mechanic Thoughts

So I'm working on dice mechanics for HotBMUSH, and I'm wondering which one is a 'better' buff, as far as mechanically: extra dice, or an increased success range? I'm looking at using either as a buff condition (or perhaps one condition for each), but I'd love some thoughts from the more mathematical minded out there.
I play a lot of Arkham Horror and it always seems that the Bless seems to be the better option; as long as you have it, it feels like it is a better buff than things that give you raw additional dice.

Increasing range nets better exponentially the higher the range goes than raw dice. Its why open d6 (WEG Star Wars) jumps from +2 to extra d6 in ability and skill development. The +3 or higher is a larger jump up.

What is your base mechanic?

@Misadventure
Right now looking at Xd6, 56 is a success, no 1s take away, no explodes, no doublesuccess on a 6. 
Then @Lotherio is correct. Lowering the target number will be multiplied by the base dice pool, and a bonus will be just that, a chance for more successes like the pool itself.
The next question is how large are the base XD6 likely to be, and how large might the modifiers be for things?
So if you are thinking 24 d6 are usual, then adding dice is going to have a large effect. If you have 510 D6, I would guess that lowering the success TN will have more effect.I would say if you want a lot of fiddly mods like cover and weapon sights and grades of tools, go with extra dice.
Something as powerful as lowering the TN would be for things that completely upgrade your performance, like a Force power or Exalted Charm, or spending a Fate point type of situation. Especially if you could do it multiple times until all your dice are assuredly successes, which can be a nice touch.
Now ultra fiddly would be computer moderated where bonuses could "nudge" a given number of dice into successes.
EG you roll 12 D6 and get 11 22 33 44 55 66. Thats 4 successes, but with a +3 nudge mod, the two 4s would be read as successes, and a 3 would become a 4, close but no success. 
The empiricist in me is asking "why not just write something that will roll and interpret the dice for you a hundred or a thousand times per test and then tweak the factors until you get results you're comfortable with"?
Human beings utterly SUCK at analysis of anything involving probability. (The ancient "Monty Hall puzzle" was ample evidence of this.) So remove the analysis from the equation and just simulate a hundred (or a thousand or a million) die rolls and see what oddities pop up.
So as an example, I wrote a quick script to test your dice. (The "roll()" function call is an external library I wrote which I won't put up for sake of brevity; it works pretty much the way you'd think it would.) It's nasty and dirty and not any kind of code I'd hold up as an example of brilliant programming, but it does the job.
The results are:
1 dice tossed  target number 1: 1000 successes target number 2: 835 successes target number 3: 666 successes target number 4: 495 successes target number 5: 320 successes target number 6: 172 successes 2 dice tossed  target number 1: 2000 successes target number 2: 1634 successes target number 3: 1319 successes target number 4: 994 successes target number 5: 646 successes target number 6: 345 successes 3 dice tossed  target number 1: 3000 successes target number 2: 2493 successes target number 3: 1984 successes target number 4: 1493 successes target number 5: 985 successes target number 6: 492 successes 4 dice tossed  target number 1: 4000 successes target number 2: 3378 successes target number 3: 2692 successes target number 4: 2012 successes target number 5: 1365 successes target number 6: 677 successes 5 dice tossed  target number 1: 5000 successes target number 2: 4198 successes target number 3: 3364 successes target number 4: 2513 successes target number 5: 1656 successes target number 6: 817 successes 6 dice tossed  target number 1: 6000 successes target number 2: 4985 successes target number 3: 3943 successes target number 4: 2955 successes target number 5: 2011 successes target number 6: 974 successes 7 dice tossed  target number 1: 7000 successes target number 2: 5813 successes target number 3: 4646 successes target number 4: 3494 successes target number 5: 2306 successes target number 6: 1137 successes 8 dice tossed  target number 1: 8000 successes target number 2: 6673 successes target number 3: 5360 successes target number 4: 4091 successes target number 5: 2729 successes target number 6: 1416 successes 9 dice tossed  target number 1: 9000 successes target number 2: 7563 successes target number 3: 6069 successes target number 4: 4561 successes target number 5: 2980 successes target number 6: 1475 successes 10 dice tossed  target number 1: 10000 successes target number 2: 8345 successes target number 3: 6706 successes target number 4: 4941 successes target number 5: 3308 successes target number 6: 1683 successes 11 dice tossed  target number 1: 11000 successes target number 2: 9209 successes target number 3: 7408 successes target number 4: 5554 successes target number 5: 3664 successes target number 6: 1866 successes 12 dice tossed  target number 1: 12000 successes target number 2: 10024 successes target number 3: 8109 successes target number 4: 6181 successes target number 5: 4146 successes target number 6: 2061 successes 13 dice tossed  target number 1: 13000 successes target number 2: 10770 successes target number 3: 8675 successes target number 4: 6538 successes target number 5: 4311 successes target number 6: 2181 successes 14 dice tossed  target number 1: 14000 successes target number 2: 11647 successes target number 3: 9271 successes target number 4: 6961 successes target number 5: 4639 successes target number 6: 2324 successes 15 dice tossed  target number 1: 15000 successes target number 2: 12495 successes target number 3: 10016 successes target number 4: 7540 successes target number 5: 5052 successes target number 6: 2479 successes 16 dice tossed  target number 1: 16000 successes target number 2: 13271 successes target number 3: 10590 successes target number 4: 8042 successes target number 5: 5310 successes target number 6: 2604 successes 17 dice tossed  target number 1: 17000 successes target number 2: 14295 successes target number 3: 11421 successes target number 4: 8537 successes target number 5: 5654 successes target number 6: 2850 successes 18 dice tossed  target number 1: 18000 successes target number 2: 15013 successes target number 3: 11957 successes target number 4: 8905 successes target number 5: 5948 successes target number 6: 3013 successes 19 dice tossed  target number 1: 19000 successes target number 2: 15864 successes target number 3: 12696 successes target number 4: 9498 successes target number 5: 6338 successes target number 6: 3226 successes 20 dice tossed  target number 1: 20000 successes target number 2: 16743 successes target number 3: 13329 successes target number 4: 9951 successes target number 5: 6608 successes target number 6: 3357 successes
From these raw results we can see a few things. If, for example, you typically throw, say, 4d6 at a target of 5, you get 1365 total successes after this thousand simulated runs. If you change the target number to 4, that jumps to 2012 successes. To equal this with bonus dice you have to go to 6 dice with a target of 5. So at 4d6 levels of dice, a 1 on the target number is equal to giving two whole dice extra rolling.
If you have 8d6 as your basis, however, things change a bit. With 8 dice tossed you can expect about 2729 successes at a target number of 5. Changing to a target number of 4 brings that up to 4091 successes. You have to go all the way to 12 dice to get an equivalent result from bonus dice. So basically doubling the number of dice thrown doubles the number of extra dice you have to throw to get equivalent effects to a single shift of target number.
Let's see if this holds true the other direction. Let's assume a basis of 2d6 with a target of 5. In the simulation that gave us 646 total successes. Lowering the target number to 4 raises that to 994 successes. We only have to go to 3d6 at a target number of 5 to equate this.
Now of course, without knowing your full intended game system, I had to make some assumptions (like that "total successes" is meaningful). If my assumptions are wrong (say there's "success" and "fail" and no stacking of success counts), I'd have to tweak my code a bit to cover the actual system, but the principle is sound: run simulations and avoid the many, many, many nasty traps of amateur statistical analysis.

If you want numbers: Anydice.com allows you to write up scripts that show the actual distribution.
@WTFE what was your final analysis as to which way to go?

My final analysis was "go whichever way has the effects you want". I gave the data (for one interpretation of the system) and showed some of the implications of it. The rest is up to the person designing the game.

OK, I just appear unable to leave this alone.
Reinterpreting the system to have only success/fail interpretation (as opposed to the #successes interpretation I originally used) the raw data looks something like this:
1 dice tossed  target number 1: 1000 successes target number 2: 845 successes target number 3: 681 successes target number 4: 522 successes target number 5: 364 successes target number 6: 170 successes 2 dice tossed  target number 1: 1000 successes target number 2: 969 successes target number 3: 883 successes target number 4: 732 successes target number 5: 537 successes target number 6: 296 successes 3 dice tossed  target number 1: 1000 successes target number 2: 993 successes target number 3: 968 successes target number 4: 875 successes target number 5: 698 successes target number 6: 438 successes 4 dice tossed  target number 1: 1000 successes target number 2: 998 successes target number 3: 987 successes target number 4: 941 successes target number 5: 817 successes target number 6: 528 successes 5 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 995 successes target number 4: 967 successes target number 5: 863 successes target number 6: 595 successes 6 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 998 successes target number 4: 981 successes target number 5: 914 successes target number 6: 665 successes 7 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 998 successes target number 5: 942 successes target number 6: 719 successes 8 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 996 successes target number 5: 957 successes target number 6: 752 successes 9 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 998 successes target number 5: 981 successes target number 6: 813 successes 10 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 999 successes target number 5: 982 successes target number 6: 829 successes 11 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 999 successes target number 5: 992 successes target number 6: 855 successes 12 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 995 successes target number 6: 896 successes 13 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 997 successes target number 6: 910 successes 14 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 992 successes target number 6: 915 successes 15 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 998 successes target number 6: 938 successes 16 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 1000 successes target number 6: 958 successes 17 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 999 successes target number 6: 959 successes 18 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 999 successes target number 6: 968 successes 19 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 999 successes target number 6: 972 successes 20 dice tossed  target number 1: 1000 successes target number 2: 1000 successes target number 3: 1000 successes target number 4: 1000 successes target number 5: 1000 successes target number 6: 974 successes
Going with my breakpoints from before, 4d6@5 gives us 817 successes, 4d6@4 gives us 941 successes. You actually have to go to 7d6 (a +3d bonus) to get the same effect. 8d6@5 gives us 957 successes against 8d6@4's 996 successes. You have to go to 12d6 to get in the same ballpark (a +4d bonus). 2d6@5 gives 537 successes vs. 732 for 2d6@4. You have to go to somewhere between 3d6@5 and 4d6@5 (the former is too low, the latter too high) for the same effect as dice bonuses (a +12d bonus).
So the same general pattern holds true whether you deal with a binary success system or a stacked success system; only the skew on the relationships changes. In general the target number is a large bonus that is proportionally equal across the board for number of dice rolled. The number of dice rolled is a moderate bonus at low numbers of dice and a negligible one at high numbers.

@WTFE
Wow. Thanks for all the input. I was running some tests differently, going through the average count success of anywhere from 2 (lowest amount dice, with the lowest starting stat and no skill training) to 14 (highest stat and skill training, no additional bonus dice buffs), as well.Total successes are meaningful (primarily in contested things like combat, where a defender's defense success takes away from the attacker's success to determine if they hit, ala many game systems; and often a task will have a difficulty threshold so count successes there would matter).
@Misadventure
That's one of the ways I was leaning on buffing powers and debuffing powers, though now that I'm looking at the success ratios on d6s, I'm now testing it out with d8s and a slightly larger threshold. I have tons of d10 charts 'cause people have picked apart the stuff for OWoD. I still LIKE d6s, but the concept of a 56 as a base success, and seeing the dramatic increase on a 46 I like, as well as the decrease when jumping it up to a 6 as the only success on a buff. I'll probably just write up the system with d6s and get some people who would want to test out the combat code for me to come through and do some stuff once I get all the buffs/debuffs codified just to see what comes out as average outside of 'white room' considerations.Again, thanks to all.

If using d6, I'd consider looking at total difficulty number vs the WoD for individual dice. Instead of day target of x successes with 5 being success each dice, use difficulty of 5 for whole pool for easy and line 25 for 5d6 to have 50 50 chance ( total of dice pool added together vs larger difficulty numbers) . I'm typing fast, hope that makes sense.

Using a total result allows each die to still matter in the end, and allows for either bonus dice, or just an addition to the total.
Note that you can use totals, and then divide by some value for simple success or health level accounting, eg divide by 3 or 5.

@Lotherio and @Misadventure
I hadn't really looked at that. I'll chuck it into the theorybin and see how it works. 
The typical approach is like so:
Assume 15 for stats, and 15 for skills, as in WoD type games.If we assume a 2 in stats, and that 2 in skill is pretty decent, thats a 4. 4D6 roll on average 14.
So we might go with the average, and say that a typical "trained" difficulty is 14. Depending on how hard it is to raise stats you might consider a truly expert problem to need 45 in both stat and skill, or you might say 4 skill, 3 stat and arrive at a difficulty based on those total pools, as guidelines.
Having an advantage could be represented by:
Add 14 to the total.
Add a D6 to the total pool.
Roll 1 more die than the total ignore the lowest 1 die.Note you could also divide the total by 5 and get approximately the same success count as counting 56 as a success. I personally like adding up totals and dividing, which makes the stink of rolling one under a success less.
But really as long as it is done the same for all characters, its a "fair" system. After that, its a question of how does it feel, how easy is it to use, and how big are the jumps when adding a die, or a +1 result.
With adding the dice, you can also do more detailed things like say that every skill level is worth a flat +4, and only the related stat is rolled.
Also: Star Wars by West End Games, runs on a free system now called D6, has lots of examples of how they handle dice and difficulties and so on.

@Misadventure
Yeah. It's a lot like the NWoD LARP methodology of 'count up to a total, divide by X, every Y past X is a success'. So we'll see. The mechanical stuff I'm not worried about 'cause code will be calculating everything behind the scenes and spitting out the output.I'm more looking at stuff that makes things like buffs or debuffs matter, and also buffs and debuffs that aren't just 'I win/you lose' buttons.