i think that the psp is better due to better games )better graphics and you can watch movies. the games are more in depth due to the fact that you can store more info on a disc. it also has ps3 connectivity, meaning you can transfer something from you ps3 on to you psp, making for a stronger support of the system. plus it has more hardcore games.
O.k... Now in that "Battle" the DS has to take the first place. DS has alot of games, just like PSP. And let's not forget that it's a touch screen, making it way more fun! You don't necessarily have to be a touch fan. btw: The graphics don't really matter, cuz comeon! The screen is so small, and the "Watching Movies" part is completely pointless when you're talking about that kind of device(PSP)!