General Kaliero
F = ma, beeyotches.
It's rather funny watching you fanboys argue.
I've been a supporter of both sides for a very long time. However, the bare facts tell me the DS will win out.
Graphics: The DS graphics are somewhere in between the N64 and the GameCube. The PSP graphics are somewhere in between the PSX and the PS2. N64 vs. PSX: N64, by just a bit. GCN vs. PS2: GCN, and this can be seen just by the same game from both systems being run alongside one another. Advantage: Nintendo DS.
Media: the DS uses cartridges, a la GameBoy (but half the size of the GBA carts). The PSP uses "UMDs" (Universal Media Discs) which apparently hold 14 times the memory of the DS. Also, the UMDs support movies. While this looks good at first, a bit of thought reveals something a bit important: Why should we care? You're not gonna be able to watch movies very well on the tiny PSP screen, and any movies worth watching will more likely be seen on your TV using a DVD player, as you can, well, actually see movies there. Plus, cartridges, though they don't hold as much memory, are the staple of on-the-road gaming for an obvious reason: no load times. Cartridge media is accessed instantaneously, while discs take time to load (and a very long time at points, as PlayStation players have seen). Advantage: Nintendo DS.
Games: A very difficult point. The PSP has Metal Gear, Spider-Man, and Tony Hawk, along with Devil May Cry (Also, possibly, the Final Fantasy series). The DS has Zelda, Metroid, Mario, and WarioWare. Both have established series and great new games. Advantage: fairly even.
Design: Well, we do know that the DS is going to have a big makeover (and name change) so it's really, foolish to comment on DS design as of yet. Now for the PSP: That's a BIG screen for a portable system. Just about the right size to get the crap totally scratched out of it. alls I'm saying. Advantage: Unknown for now. Possible, though unlikely, that Nintendo will design a worse one than the PSP.
Release: Ah, the all important release... DS: this holiday season. PSP: NEXT SPRING! Lemme tell you somethin', guys: That does NOT help Sony. Sorry. However, I doubt Nintendo will get the redone DS out by November (as the say), so I think the launches will be about equal. Advantage: Unknown, but probably none.
Price: DS: probably around $150, probably just a BIT under. PSP: from the way spokespeople dance around the question, it'll probably be MUCH higher. And despite the fact that disc media costs less to make than cart media, don't even START to think Sony will sell their games for a lower price. Advantage: Nintendo DS.
Verdict: The DS will win out, simply because Nintendo is thinking intelligently, and relying on gameplay instead of hype and stats-on-paper.