It depends on what you're looking for, I guess. Take everything that follows with a grain of salt, as I'm a nintendo fanboy, and they can do no wrong (aside from the Virtual Boy).
The PSP is pretty much a PS2 you can carry around in your pocket. Its got a *huge* screen, and the colors really pop. There are some good games (lumines is the only one that comes to mind, metal gear acid was fun until I beat it 5 hours later). The PSPs problem right now is that there are Zero good games out for it that aren't ports of PS2 games. The most fun I had on mine was loading old nes and snes roms onto the memory stick and playing those. Sony, however, seems hellbent on stopping the fun with firmware updates. I sold mine to a sucker who doesn't want to play anything other than GTA 3: redox.
The DS is the shit. The stylus is a good addition, and there are scads of good games (warioware: touched, feel the magic XX/XY, trauma center, Pheonix Wright: Ace Attorney, Castlevania: Dawn of Sorrows, Metroid pinball, Mariokart DS, Advance Wars: Dual Strike, et cetera). The battery life is better. It plays my GBA games. The only leg up on the DS the PSP has is its graphics, and its an MP3 player (well, sort of, its an ATRACC player).
If the idea of playing games that looks somewhere inbetween an SNES and an N64 makes your skin crawl, get a PSP. If the idea of paying 300 bucks for a machine that will let you play GTA3, and watch meet the fockers makes you laugh, get a DS.
Try to find a friend with each, though. Thats the only way you can know which one arrouses your interest.