Lol, if you want a non-biased answer, this is the best I can give you. It simply comes down to personal preference.
Do you want a handheld just for games? The DS, unlike the PSP, has no cool features. It has a few applications like a calendar, clock, alarm clock, but nothing cool like the PSP. However, the DS has much better games, in my opinion. So if you want a handheld for pure gaming, get the DS.
Whereas the PSP has some good games, the DS has even more good games. But on the other hand, the PSP has more to offer. You can watch videos, play music, also the homebrew is so much better on the PSP. Plus if you have a PS3, you can do some cool stuff with your PSP.
For pure gaming, get a DS Lite. For media-pleasures and homebrew, get a PSP.