Yes.
Oh, wait, I meant no.
Welcome, casual reader, to Game Design 480: Character Stat Foundations, an advanced course about what statistics to include in your game. Should you have stats derived by adding and dividing other stats together? Should you have core stats with a list that enhances or affects them? Skills? Attributes?
Firstly, what do we mean by Attributes? We mean the pinnacle stat, usually used to describe the character's raw capabilities. Strength, Dexterity, Stamina, Charisma, Intelligence, Wisdom. They are almost never, ever skills, which tend to be specialty items that are learned or trained. Okay, yes, you can train up your strength but as a person you tend to have limits. Attributes are before what you can learn to do; they're what you are.
I'm going to skip D&D because we should generally all get the gist of it. Skills came to D&D very late (about four versions in with 3e, tho they existed as an option in 2e). Skills are a secondary consideration as the original D&D the Attributes were never rolled, ever. They were the basis of table-lookup derived skills like "Bend Bars/Lift Gates" and "Saving Throw: Poison". Even now, I think D&D and Pathfinder half-ass it, but they half-ass it in a very comfortable and predictable way, so it's a good half-an-ass.
Paranoia 2nd Edition, Toon, and Teenagers from Outer Space all had a system where there were skills under a broad category, those categories not always but often considered to be attributes. "Chutzpah" from Paranoia being my favorite. You would add the head stat ("Chutzpah") with a subordinate stat ("Spurious Logic") to see how well you could do, but it was always "Chutzpah"; you could not link "Spurious Logic" to any other attribute.
Again, similar to D&D, tho many other games did it this way first. Everything Chaosium, for example. In this way, you had a pinnacle stat, skill or otherwise, and all its subordinate skills and abilities.
The Storyteller System (the original World of Darkness books) said, "Hey, you know, what do we roll if someone wants to recognize a gun by sound in the distance? Wouldn't they link their Firearms to something else in this case? A perception attribute we might call 'Wits'?" I'm sure other games asked the same question beforehand, but please forgive me as I'm not sure who. Possibly Shadowrun. Anyhow.
Around this time, and a little before it, a game system known as F.U.D.G.E. took the opposite notion: Let's just focus on the important stuff, the things you know and the things you can do. Okay, in FUDGE they had Attribute + Skill systems, and it took Fred Hicks to say to whomever he was driving home from a convention with at a time, "Seriously, why Attributes?" And so FATE was born.
FATE as a system goes entirely into the idea that what you can do is all that needs recorded. It doesn't matter if you're super-melee-god because you're strong, or quick, or both. You decide why it is; all that's important is that anyone getting in your way is likely to end up with a bloody nose.
Even further abstracted, this kind of "ability instead of attribute" game can be played this way: Invent your own abilities, give them numbers, and play. "Fire Magic: 3", "Pew Pew Pew!: 2d6", so forth. God help me that I can't remember the game that @WTFE loves so much in this venue.
Which leads me to answering the question in this thread. All methods have benefits and drawbacks, so much so that there's no one that's better than the other.
I'll play all of these, complain about all of these, and try to encourage everyone to play to the spirit of the rules depending on whichever one is used.
I prefer the abilities-instead-of-attributes-and-or-skills of the FATE/Fate Core method. I want to be the one who decides if my ability to bitchslap comes from being wiry or brutish or skillful. Maybe I have rapport with spirits because I'm a good bullshitter, or because I'm bat-shit crazy. Unfortunately Fate Core is such a high-adventure game that I want to see a low-power version for other kinds of play.