If you want to play Nintendo games, go with the DS. If you're looking for anything that doesn't have to do with games, go with the PSP. If you want to play some games (depending on which) you can either go with the DS or PSP.
I personally like the DS more. You've got to be more careful with which games you buy since a lot of Nintendo DS games are massive disappointments. I used to have 30 games in total but have cut down to just 10. PSP if you want a lot of games, but I think that DS brings a lot more innovation in their games and incorporates some pretty original features. It's a lot cheaper too.
Cheaper, more inventive games, a touch screen and there's games still being produced for DS (granted, that applies to PSP too, but with the release of the PS3, PSP production has almost ceased) - the DS is just a great console and you certainly should not go for the DS just because the games look prettier.
