I think that's an interesting question. Myself, my background is in tabletop gaming. My dad introduced me to Paranoia at age 5, and I was hooked ever since. Not to say that I haven't been playing computer games since the DOS days, just that I cut my teeth - so to speak - on tabletop games first.
Really, that's kind of a paradox that exists with videogame RPGs in general. I mean, if I'm playing a game of Dungeons and Dragons for example - it takes years to get from level 1 to level 20. In those sort of games, that degree of progression represents your character starting out as a young adventure and then retiring as an old weathered veteran. In a videogame like Fallout 3, you go through the same degree of progression in (it depends on how much time you play at once, of course,) say a month or so?
In short: in a tabletop RPG that amount of character progression represents virtually the entire scope of that character's life over the course of years or even decades. In something like Fallout 3, you're going the same distance in what amounts to a few months of the character's life.
For me, it's just one of those things I try not to think too much about.
For a more generalized answer, though - I tend to see my player character as pretty much the same as anyone else. What tends to separate them is a degree of determination and simply being a born survivor. Any other NPC could potentially progress and gain experience by doing the same things as my character - the difference being that my character actually is doing all these things, while most of the NPCs aren't.
ie, after getting beat up and shot to hell and back by raiders after scavenging at a run-down school, my characters tend to be type that after healing go back out to do it all over again, whereas your average person would likely just call it quits at that point.