I made a passing comment on RPGnet that, given the statement that D&D is about "killing monsters and taking their stuff," you could sum up the old school and new school perspectives as a split between focusing on killing monsters (new school) versus focusing on taking their stuff (old school). It's not entirely a joke, especially if you broaden the two terms into "action" vs. "acquisition".
It's been said that New School D&D is about character challenge, which is what I mean by "action". People who prefer new school prefer knowing what their characters can do and whether they stand a chance doing it. In other words, they look for lists of well-defined skills and powers, as well as balancing encounters against party strength. It's all about being heroes.
Old School D&D is about player challenge. You have something for your character to acquire, and it's up to you to dream up the best way to get it with the least risk. In old school, classes are meant to limit rather than enable.
This applies to a whole lot more than just D&D, but there's plenty to discuss in any case.