You technically have already answered your own question. The DS is for someone who wants innovation in their gaming, while the PSP, which sucks, is for the troglodytic idiot that has been fooled and completely ripped off by Sony's ignorant endorsements by celebrities who want the support of a major electronics company due to the lack of their popularity. I think that through my reply that you know that I am officialy a Nintendo fanboy, but for the reason of believing that gaming should not be ruled by idiots who don't understand it, but still win only because of humanity's dullness with their intelligence and that it should be ruled by a company who actually cares for their customers. Oh, by the way, (I went off track) the DS is just better only because of the company that runs it and the companies who will, I hope, finally realize the true potential of a handheld as being a major asset to society's gaming.
It is true the PSP has much better graphics and more features than the DS, but is it ruly worth $250? The DS has innovation, fair graphics, and is a little more sturdy than the PSP. It is also about $100 cheaper. Which is better?