Alamak! Another one!

It depends on your preference.. the most important factor of all: GAMES. Buy the handheld which has games you like.

Now.. PSP has extra features such as surfing, media playing which includes MP3's and videos.. If you feel you need to have those.. Then the PSP may be for you. The PSP is also a powerful handheld.. So you'll get shiny graphics like those games on the PS2.

For the Nintendo DS.. It's just games games and more games.. If you like to play something interesting which can't be emulated/played on any other platform.. Then.. the DS may be for you. The graphics compared to the PSP on the DS is way lacking.. Looking like a finer-tuned PS1 game. But don't let that stop you from buying a DS.