Shooters :
Socom and Syphon Filter >>> Metroid
SOCOM really wasn't that great, the campaignucked, and the online play is it's only redeeming feature but wasn't that great because of auto-aim. Haven't tried Dark Mirror, but it has gotten good reviews, so it stacks up as a good PSP shooter.
On the other hand, Metroid has a lacklustre single player, though still pretty fun, albeit short also. But it's main component is online which is much better than SOCOM's for aiming features and the fun factor.
In the end, I'd say they're about even. Goldeneye DS and Coded Arms cancel each other out in this category (though Goldeneye is better).
Platformers :
Daxter, Mega Man : MHX, Mega Man Powered Up < New Super Mario Bros, Kirby:CC, Sonic Rush, Castlevania (Only by a hair)
Only by a hair!? You're kidding, right? Mario alone destroys any PSP platformer. Kirby was great fun, especially in the early life of the DS when there was a bit of drought of games. Sonic was great, finished it. Castlevania was brilliant - one of the best games for the DS.
Daxter isn't nearly as great as the Jak seris (which IMO aren't that great either). Thouh MHX was excellent, especially for a Mega Man fanboy like me. It was just too short. Day of sigma kicked ass though. Powered Up wasn't as good, but the characters and level downloads/maker were awesome while the fun factor lasted.
I'd say the DS definitely wins this.
Racers:
Ridge Racer, Burnout, NFS, Wipeout >>>> Mario Kart DS, no matter how cool it is.
Mario Kart is the best game on the DS, but you're right here. PSP is doing a lot better with driving/racing games. PSP's RR and Burnout are far superior to their DS counterparts.
RPG's:
Kingdom of Paradise, Legend of Heroes, Monster Hunter = Mario and Luigi: Partners in Time, Animal Crossing(Both systems are sucking though)
Kingdom sucked, LOH sort of did, and Monster Hunter I don't know about, dosn't interest me. Popolocrois was great though, that should be included in the list. M&L wasn't nearly as good as the first one, but by no means bad. Animal Crossing is excellent, though the online element isn't as great as I hoped for. At least Nintendo sends you stuff.
I don't know about this category. I think equal is about right, though if Animal Crossing was better online, it'd make the DS win.
Strategy:
MGA!, MGA!2, Field Commander > Advanced Wars
This is true, MGA! series is very cool (not as good as regular MGS, but still). I never got into Advance Wars anyways.
Sports:
Should I bother? PSP >>>>>>>> DS
Yep, this is completely true.
Innovative Games
Should I bother? DS >>>>>>>> PSP
Again.
And as far as puzzle games go, Meteos destroys any PSP puzzle game, even Lumines.
Upcoming games:
MGS, GTA, Tekken, Silent Hill, FF, R&C, Loco Roco >> Yoshi's World 2, Starfox, Diddy Kong racing.
Your upcoming list certainly shows a bit of fanboyness. You neglect to mention several of the DS's best titles.
Along with YW2, SF, DKR, there is Zelda: Phantom Hourglass (which looks amazing), the new Castlevania which will surely own like the first one, FF3 (which will be incredible), Tales (not a port like the PSP one), the new Pokemon games (which haven't been as great the past few attempts, but perhaps they'll break the trend), and finally a brand spanking new Mega Man game - not a remake.
On the PSP's side, MGS: PO will surely own, GTA: VCS will hopefully be just as good as the original VC, Tekken looks like ****e to me, Silent Hill should be good, and FF? You mean Crisis Core...? Haha, ok. Ratchet and Clank hasn't really been good lately. The first one was the best, and I'm not really hyped for the new one, Loco Roco is... odd?
Now throw in GTA somewhere, Better graphics mixed with MP3, and PSP > DS. The only remaining plus for DS is it's price.
GTA is surely a plus for the PSP, but LCS is headed to PS2, so VCS could head down the same route. Better graphics are without question but they certainly don't make a game, MP3 - I'd much rather use my Zen Micro, thank you very much. DS has more pluses than just price, how about better games and the kick ass DS Lite?