Another perfect post Lanefan.It's a question of focus.
If your focus as player is first and foremost on mechanically advancing your character through level-ups, new powers, feats, etc. you're probably much better served by any of the WotC D&D versions as that's what they do.
In old-school gaming, at least the way I see it, advancement is a somewhat secondary consideration. Sure you level up now and then but there might not be much mechanical impact (and even less in the eyes of the player, as the nuts-and-bolts mechanics are largely kept DM-side), and therefore it's not as much of a focus. Instead, the focus is more on the here-and-now in the fiction - how are we gonna get into that castle, how are we gonna knock off that giant, how are we gonna get all this loot back to town - rather than on the broader metagame of mechanical character advancement.
I’d point out that which system you use doesn’t really matter for this definition of Old School. You could probably work into this feel in many game systems. Myself, I’m always going for “1st Edition Feel, 3rd Edition Rules” in running my 3.5e campaigns with classic 1e & Basic modules.