I have both and they both have their ups and downs.
I mostly prefer DS because it's easier to carry around, but PSP does have some nifty features and some good games aswell. The real problem with PSP is that when playing from a disc the system can be quite noisy plus the fact the loading times are really long when compared to DS games. But DS lacks as good graphical capabilites, but it does have more ways to play a game just because it has a touch screen.
Also with PSP it's annoying that the battery runs out more easily, because it afterall is disc based and spinning that disc requires a lot more power than just reading data from a cartridge.
I mostly prefer Nintendo DS. It has literally won the markets and has more good games than PSP, while PSP is still quite good handheld console.