I have both (Again

) and love them both. They both have thier unique qualitys really...
DS: Games are colourfull, bright and have a great sense of fun. Looks great and has a sense of carelessness about it. (As in you can be a bit more rugged and chuck it in a bag etc) You can play movies and music with max media player or the like but movies are not great quality. Aimed more at the younger market.
PSP: Technically better, awesome graphics and sound, techicnally superior games especially driving games. It looks amazing... I actually forgot how good the screen is. Plays movies and they look stunning (You can now buy movies for as little as £6 each!) Surf net, play music and other videos. Aimed more at the older generation of gamers.
So if you like games that are a little more fun go for the DS... With stuff like advanced wars, new mario bros, mario kart and a new zelda coming you are on to a winner...
But if you like eye candy, great sound, and love games that are technically better such as Tekken, Syphon filter, GTA and aparently a really good conversion of MSG then the PSP is for you... (Oh and there are rumors of a psp version of resident evil oubreak with online play! YEY!)
Oh but 1 more thing about the psp... Where the heck is Gran Turismo Mobile??? I am sure there will be a lot of really annoyed ppl that have bought a psp and this doesnt actually emerge...