It all depends on what games you like. I own both, a DS Lite and a PSP (fat). I like the DS Lite for a few games, such as the GBA and DS Castlevania games, Mario Kart DS, and the Bleach games, but my favorite genre is racing games, and the PSP is the clear choice for that genre, with games such as Burnout Legends, Burnout Dominater, Ridge Racer, Ridge Racer 2 (Import), Crazy Taxi: Fare Wars, Outrun 2006: Coast 2 Coast, WipeOut Pure, WipeOut Pulse, Jet Moto (PSN), Jet Moto 2 (PSN), and WipeOut (PSN). Also, since I don't have the kind of money to afford a Zune or iPod, the PSP does a decent job as an MP3 player. But if you get either a DS/DS Lite or a PSP/PSP (thin), you owe it to yourself to get Space Invaders Extreme.
Oh, if you go for a DS, get the DS Lite, even if you have to get the pink one, the screens are so much brighter, it's well worth the cost, and if you get a PSP, get a slim; it has more RAM (for faster loading.. for games that are programmed to do that..), the D-Pad is more responsive (for fighting games such as Tekken: Dark Resurrection, Tekken 2 (PSN), or Street Fighter Alpha 3 Max..), and the battery life is longer on both slim PSP and DS Lite.
But if I had to choose only one or the other, I'd grab both and shoot my way out.