I love my DS Lite, I play New Super Mario Bro's, Super Mario 64 DS, Brain Age, Mario Kart DS, Zelda A Link To The Past for GBA and Super Mario World 3 for GBA. I don't own a PSP but I have played my buddies and kiosks. My biggest gripe about them is the loading times, by the time the games have loaded (at least the ones I have played), I lose interest and don't even feel like playing anymore. Maybe I'm just impatient.
I do however still want one if only for the multimedia purposes, but I would defiantly play my DS more than I ever would a PSP. When I play handhelds I want to play mario, tetris, things of that nature; if I want to play GTA or NFS, I jump on my 360. Note about graphics - the PSP obviously has an advantage in that department, but imo, the DS has the better games, and thats what really matters.