I think it's reciprocal. To my mind, PCs are going to be a bit better than everyone else (there's something about them that's just inherently above average). It gives them an edge, but there are people who're even further above average, somewhere. That makes it possible for them to do what they do; if the average campaign is an accurate reflection of adventurer mortality, then everyone would be signing up if they could (I'm estimating roughly 50% mortality as a highish value), if only for a couple of weeks. The rewards are just insane. But training and experience are even more important; a level 1 Warrior with straight 18s is going to have a tough time with a level 2 or 3 Fighter, even. But the only way to get that training and experience is by hero-ing. And the only way to survive your initial attempts at hero-ing is to be a bit better than everyone else, or be extremely lucky.
PCs would have, ideally, a few advantages; higher ability scores, maybe PC class levels if we keep the distinction, max hp at level 1, and maybe action points if you use those. It's actually a slightly false distinction, though, because some NPCs, somewhere, are going to have all those things or better, too. If you want the "rise up from wimpiness to true heroism" aspect, lose those advantages at character creation and either never get them, or have them gained gradually as the campaign advances. At any rate, such things need to apply to the whole party equally, if you need to see that aspect of character growth reflected mechanically. Otherwise you get Elfy McWizardpants doing his thing, making John Expert look like a real idiot.