Racing=Either. They both have good exclusives and share many multiplats. It's a wash.
Sports=PS3. Now that EA got their act together on PS3, I will give PS3 the nod for MLB and NBA series.
Shooters=360. You can't use future titles to tell everyone PS3 has better shooters. Killzone isn't coming out for another six months. 360 has better shooters NOW. No need to dabble in the future.
Platformers=PS3. I'm assuming we're not including the Wii in this argument, otherwise the Wii wins hands down for Mario Galaxy. Ratchet and Clank is a better selection than the Crash Bandicoot and Spyro nonsense 360 has been getting.
Puzzle Game=360. Echocrome is one game. Xbox Live has so many good puzzle games I could go on a very long list to explain away Echocrome, but I'll leave it simply as 360 has Braid. End discussion.
Best Action/Adventure=Either. Uncharted is great. So are Dead Rising and Kameo.
Best RPGs=360. No need to argue this one.