They both have their good points. I personally own a DS lite AND a PSP so I'm going to do my best to help you.
DS lite: Excellent system, alot of game choice. Like, ALOT of game choice. Not only that but if you're like me and you still have some GBA games laying around you still love (like old Pokemon ones or for me Zelda games) then I'd definitely choose the DS. I wouldn't waste the money on a DSi, but i guess that's only if you're partial to the GBA slot.
PSP: Not as much in the way of game selection, I got it because I can't afford a PS3 and release of Final Fantasy, Kingdom Hearts, and Persona have been announced/published for it. I find that the PSP is more of a specialty system, you really only see people buy it if they know ahead of time what they want. There's also the added bonus of it being a music player for me (and a video player for others) so if you're looking for something that's mroe content oriented and less about the games themselves (not to say there aren't good games for the PSP but there is a far slimmer market than the DS) then I'd vouch PSP.
I really hope this helps!