I would say you should know what you're looking for in a handheld when comparing the DS and PSP. Keep in mind I am a DS supporter and a PSP, well, non-supporter and I'll tell you why. I love old-school RPG's and there is not a single platform available right now with a better selection. The PSP is going to run more towards the action oriented type of games, at least the top-end games are pretty much action oriented (GoW, FFVII:Crisis Core, Resistance: Retribution, the GTA's, etc.) Also, if you're looking for a multimedia device, the PSP is going to be much more capable for that. The PSP is also a graphical powerhouse of a handheld.
But, again, I prefer the DS for the input (a single analog is just not enough), the clamshell design which protects it so much better, the games being more up my alley, and the fact I get to support the big N.