PSP has mostly ps2 ports, so u have to like ps2 to like the psp. PSP in my opinion is also a lot more delicate ( I take care of mine, but this guy at my school dropped his and it craked the screen, well not actually the screen but the think-plastic that covers the screen on the psp( it kinda surrounds the whole psp actually thats why the psp looks transparent at some angles.)
DS, has a lot of fun games and has the best handheld game series of all time, pokemon. One of the only "handheld" game series to actually compare in the charts with the big consoole blockbusters. Its also more sturdy.
But u also have to take into consideration that psp has all the added media features and u can turn off a game at anythime and then turn it on again and u will be at the same exact place in the game, its my personal favorite thing that i love about the psp.