I've had both...
First I had my phat DS, then sold it because I didn't like the games that were out for it. (Well the DS was just out so...) So I traded it for a new PSP... Although I downgraded its firmware and stuff I wasn't really satisfied with it. There were only few games that I actually considered playing, and with only a 2GB memory stick... well you can imagine... ^^
Then I got me a new DS with a M3 flashcart after finally finding out that playing roms on your DS is even possible. In the meanwhile there were a lot of good games that came out for the DS (I love RPGs
) and I could still play my favorite GBA games, as well as all the good SNES and GBC games using emulators. Then there was a lot of great homebrew, even a browser (it's not that good though, but good enough to have a look at your emails and forums and whatever) and what I like best: Colors!
You can play MP3's, OGG format, and even videos on it, have a look at your photoes like you could do on your psp as well, but the NDS STILL has the TOUCHSCREEN that makes it really unique and offers a lot more possibillities.
Even a whole PDA...
So being stuck with all my favorite Nintendo games and only having a few faforite games on PSOne I definitely say that I prefere the DS in any case.
As you can see the graphics in newer games even have improved. It may not be as great as on a PSP, but it's still lovely and fits my taste much better.
(Although I have always wished for a Zelda OOT adaption for the DS... That would have rocked!)