For a long time, I have believed that Old/New School in roleplaying isn't a problem with the rules, it's a matter of approach. I've been through several iterations of this theory and finally pared it down to a simple statement.
Old School is an adversarial relationship between the player characters and GM - the GM is an active obstacle to the (inevitable) success of the player characters. New School is focused on a collaborative story between players and GM.
That's my belief. The only difference is how the story is created. It is possible, and even likely, that in each scenario a party of ragtag misfits save the world, destroy the evil wizard, and rescue the fair maiden. The difference is in how that scenario is crafted: Old School will involve a list of notes or a published adventure including a list of things the PCs must accomplish before their final goal (defeat monsters, solve puzzles, overcome traps, talk past guards), while New School will change and alter the world around the actions of the PCs (if they check for traps, there will be traps; if they rush through a dungeon throwing caution to the wind, there will also be traps).
Rules have nothing to do with it. Some settings and rules lend themselves more towards one school of thought than another; Don't Rest Your Head's dice-lite system lends itself more towards the New School, as it doesn't rely on a hero's skills and abilities so much as tendencies, while All Flesh Must Be Eaten gleefully concedes that there's no way a party could prepare for every eventuality.
I think every group falls close to the middle of Old/New, and we're only aware a disparity because every system that comes out is, in its own way, an attempt to improve the way we tell stories, and they accomplish that in different ways. 4e is an Old School system because it has a lot of ways to hurt the PCs, while Fate is New School because it does not try to come up with everything.