The 360 is the most weighted towards the genre. I'd go on record and say that 4 of the 5 best selling games in 2009 will be the following:
Halo ODST
Resident Evil 5
Call of Duty 6
Halo Wars
Of those 4, 3 are shooters. Last year, the top 5 games released on 360 were:
Gears of War 2
Grand Theft Auto 4
Call of Duty 5
Fable 2
Rainbow Six Vegas 2
So 4 of 5 were shooters last year, and it's entirely possible that the same will happen again this year. Of course, these shooters do take different flavors: some are first person, some third, some are spiced with "sandbox" play, but if you don't like picking up guns and shooting people, the vast majority of the big games on the 360 won't interest you.
With all that said, I got plenty of use out of my 360 last year (I enjoyed Fable 2, Ninja Gaiden 2 was disappointing but still fun, Braid was my GotY, Castle Crashers was fun, and I love Netflix so so much), but I recognize that my tastes are eccentric for a 360 gamer and for the major blockbusters, the offerings are fairly skimpy if you don't like to blow stuff up. I don't think this is much different than minigame compilations for the Wii: they come in different flavors (sports, party, theme) but if you dislike the genre you're in trouble. I'll do a listing of those in just a second.