For it's intended purpose (playing games specifically designed for it), I prefer the DS as right now it just seems to have the better game library. (PSP tends to have a lot of ports but not as many cool original titles).
For purposes other than what it's intended for (read: hacks), the PSP destroys the DS. A hacked PSP can run games for systems up to the PSX through emulation (or natively, in the case of the PSX). Also, the third party medioa players and utilities are amazing. GPS, Streaming radio, playback of various audio and video codecs, the PSP does it all.