I've sat back on this topic a good long while, so of course, my opinion is worth more (I say, I say, that's a joke, son).
I tend to think that the difference between an NPC and a Staff PC (or GMPC or whatever you want to call it) is that an NPC serves a purpose that is not simply engaging in RP. That purpose may be dispensing plot info, it may be guiding PC leadership/PCs away from unthemely decisions, it may be generally reinforcing theme, it may be... well, there's a lot that it may be, but it should, in my opinion, always be something more than simply engaging in RP. That doesn't mean that they can't be involved in BarRP or come to a PC party, but they should always have a purpose in doing so that goes beyond their character. And while it might be fine to introduce an NPC in an awesome way to prove their bonafides as a source of info or an authority figure or whatever, besides maybe that one exception, they should never be the spotlight of a scene.
A Staff PC, on the other hand, is there to engage in RP, often focused on their own story. They may be used to dispense info, they may be used to give nudges into more profitable courses of action, and they may be used to reinforce theme, but their focus will be on engaging in RP, rather than serving any other particular purpose.
I fully believe that Staff should be allowed to -- nay, encouraged to -- have PCs on their game; I don't believe there's a better way to keep your finger on the pulse of the game than playing it. I've learned that Staff PCs should never hold the spotlight even as much as the average "engaged" player, and certainly well less than the most-engaged non-Staff PCs. I believe they should never hold any position more important or rare than any other PC (and usually nothing that several other PCs don't already hold). I believe they should never save the day, except in the company of others. I believe they should be within the bounds of an "average" PC in every way. Is playing a Staff PC less fun than playing a non-Staff PC? Probably a little, because you have to be careful that there's no perception of unfair advantage. But that's part of the price you play for having a game that is (or should be) exactly what you want to play.
An NPC, on the other hand, can be the One True King (to keep all the PC nobles from instituting direct democracy in what is supposed to be a feudal game or to keep the peace between squabbling PC nobles in what's supposed to be a PvE game), an ancient sorcerer, a computer superfreak who knows just about everything committed to electrons ever, or whatever awesomeness the plot/setting needs. They can have skills, powers, or rank that no PC can have, because they're a mechanism to enrich the story of the PCs. In my opinion it's fine to have scenes where an NPC is just there to be social -- it can help show who they are, and give context to their other, more plot-driven actions, but I think that the majority of their scenes should be driving plot or reinforcing setting.
Focusing on 1-2 PCs with a single "important" NPC is a good way to get the rest of the playerbase thinking that they're being spotlighted to the exclusion of others, whether the NPC is teaching those PCs, TSing them, or shooting craps with them, it's just bad optics.