I've owned both a PSP and a DS lite, and I'd definitely recommend the DS. The PSP does have much better graphics, but in my opinion it was difficult to hold and cramped my hands after awhile. That being said, there are some advantages of the PSP. RPGs are a big one, as they don't require that great of control, and the graphics really do improve the experience. First person shooters, oddly enough, also seem to be better on the PSP (probably because DS only has metriod prime hunters, which isn't really that much of a 'classic' FPS anyway).
Other than a few standout games however, the PSP is very difficult for a handheld. With the DS, you can close it any time, no matter where you are in a game, and it will automatically sleep at that point (effectively pausing your game until you're ready to play again). This makes it great for playing for five minutes while waiting for the bus, or other times when handhelds really shine. The PSP however, takes some time to sleep when you're done playing.
On the other hand, if you're looking for a jack of all trades machine (and you don't already own an mp3 player), the PSP can be rigged to play some great emulator games, and if you have the money you can buy a very large memory card, to load all the emulated games you want. You can play a few mp3s from it, but in my opinion a normal mp3 player is better. And finally, the movies look great on a PSP. But personally, I would rather watch them on a computer or TV.
So remember, if you just want games, DS is the way to go, if you want something that can do everything pretty well (not exceptionally, but just pretty well), you'd be happy with a PSP.
