I don't think the graphics should set it apart. The type of Genre I look for state of the art graphics are FPSes.
PSP Wins for FPS Mode
The DS has the touch screen with a stylus. Here's a phrase for you. Hand-Held RTS. Thats gotta be a point for the DS.
RPGs? Graphics aren't everything here. IF they were.. whats up with all us D&D freaks?
If you've played Golden Sun, then you'd agree you don't need state of the art graphics to enjoy a very... VERY well done Console RPG.
When you think about it, There is a wide range of games that will excell on both systems equally as well because of their bonuses.
PSP will excell in games that require great graphics. So I could see PSP for being good for FPS style games on the go. That would make me want to buy it just for that. To be able to play a FPS whenever I want. Then be able to link up? Yeah that'd be cool.
Then if you look at all the possibilities of a Touch Screen on the DS.. there are many types of games that will also only excell on the DS. I mean the screen in and of itself will become THEE most universal button EVER known to a gaming system. RTSs, Chess styles, Drawing (heh, Mario party with 2,000 people at the same time.. pure madness.. MADNESS I SAY!)(remember the internet hub idea), Simplicity such as choosing your plays in a football game.... the possibilities with this touch screen is just so insane that I have yet to find an ending.
In the end? Both will be great systems, and both will have abilities that they will excell in more than the other. So plan on buying both, but figure out which options between the two appeal to you most.. then get that one first.