I play both my DS and PSP equally, but both for different reasons.
My DS is nothing but a game system, but it excels at that. I have tons of games on it of various genres and I really enjoy it.
My PSP is nothing but a game system as well, but I use it primarily as a way to play roms of the old games I own. I love my old games, but I live in a tiny apartment and couldn't bring them all with me. I also have some original games for my PSP, which I enjoy as well. I just can't find as many original games I want for it as I can for the DS. However, if you like handheld sports, racing, and shooters with crappy controls, then you'll find plenty. My favorite genres are RPGs, Platformers, and Action-Adventure games, which the PSP is a bit lacking in.
So, I would say it really depends on what you like. Both are great consoles, and I'm really glad that I own both.
