I have both, but I enjoy my DS far more than my PSP. As mentioned before, the DS not only plays DS games, but it also plays GBA games, and that can result in many potential games to enjoy!

PSP is definitely better in multimedia, but everything it does, I can do already without it, so I feel kinda sad about having one now...

Anyways, I also enjoy the touch-screen capabilities on the DS, and having that extra screen kind of results in a more immersive game experience. If you want games, go for DS. If you want a portable media device, go for PSP. In the end, it's what you want, after all.