I've got a Nintendo DS. I looked at the PSP and really love the larger screen, but couldn't find any PSP games that I liked. I'm not into sports games or fight games. Considering its capabilities, I'm surprised how few first person shooters there are for it. I may still get one at a later date if the right games come out.
In the meantime, I'm happy with the DS. There are some good games out for it now, and
Metroid Prime: Hunters is on the way. The other thing you may want to know is that the DS goes longer on a battery charge: ~6 hours for the PSP as opposed to ~10 hours for the DS.
What I would suggest is to browse the
DS game list and the
PSP game list and see which games interest you more.