I had at one point both a DS and a PSP. I do not believe that they can both fit in the same category as there is a market for both. The games I can get on the PSP, is not at all possible on the DS and some games on the DS are not possible on the PSP.
The PSP is more focussed on people who want high grade/'higher definition' handheld graphics. A miniature full fledge console and are willing to pay for it. Games such as Ridge Racer, Chains of Olympus, FF:CC etc define the PSP. Exceptions are Patapons and Locoroco.
The DS is a casual, low qual graphics cheaper console that most casual/pokemon gamers would require. I believe there is a higher market for people who just want to chill out on their spare time with a small/less intense game which is what the majority of DS games are like. Titles like brain training, Pokemon, Cooking Mama(!), Layton etc, define the platform norm. Exceptions of course are Dragon quest for example.
All in all, depending on your taste, both the PSP and the DS might fit for you. Apart from the fact that they are both portable, there is nothing really similar to both. They can co-exist.
I am a Gamer... I play games and not consoles. I have a PC and Console on which I game... I like games. End of Story!
