DS Pros:
Touch Screen, Unique Feature. Games that use the touch screen are the best games on the system.
More Portable, Both the games and the system hold up better for pocket travel. DS games are almost indestructable. Also the Clam Shell design protects the screens.
Internet, The Internet browser is better because of the touch screen and dual screen, Its more easily navigated.
DS Cons:
Shovelware, Being a popular system means that everyone and their brother produces games for it so there is a hi signal to noise ratio.
Graphics. Yes the resolution is poor, and the 3D isn't very detailed.
PSP Pros:
Graphics. It has the widescreen and higher resolution and better 3D graphics.
Other Uses. It does music and video
PSP Cons:
Ergonomics. Games that are PS2 ports or similar make my hand cramp up because of the analog nub. Its really bad placement.
Fraglity, UMD break if you look at them wrong almost. Also the loading times aren't nice for a portable system.
Extra Cost. In order to save games on the PSP you need to buy a Sony Memory card. Thats extra cost on top of the system.
They each have good points and bad points But I like the DS better. Yeah it has kiddie games, but does have some very excellent games.