I like Double-Screen better, it has touch screen, and you could play 2 games, not at the same time of course. 2 games because there are 2 slots, one for DS, and one for...err, something!
psp it has so many diffriant things that you can do with it, and there are so many new things coming out for it. there is going to be psp to psp phone calling and a gps application for it
i rather psp.. you can put music on it files videos and can also put games on it .. and if you got ps3 you can also connect with it and can talk in chats and more .. well if you got ps3 its really awesome.. only diffrence is DS has touch screen and some games are more fun too play on DS but on psp you can do alot more