Personally I love shooters. So with Halo3, Gears 1 / 2, Left 4 Dead the Xbox360 is the right choice for me.
But I don't think that is all the Xbox360 can deliver. There are great RPGs like Mass Effect (even though I did not get into it) Fable2, Lost Odyssey, Fallout 3 + DLC, Infinite Undiscovery (it is better than people want you to believe), Tales of Vesperia and the upcoming Star Ocean or Final Fantasy XIII.
The casual market is not as big as on the Wii, but with Scene it(2) / Lips / you are in the movies / Rockband / Guitar Hero there are some games you can have fun with
Plattformer like Banjo Kazooie or Viva Pinata could keep you busy as well.
Survival / Horror games like Condemned (2) / Silent Hill / Resident Evil 5 / Dead Space / I Am Alive or Alan Wake are already available or will be available soon.
With PGR 3 and 4 / Forza Motorsports 2 (soon 3) / Race Pro / Need for Speed / GRID etc there are more than enough racing games out there.
So there is not one genre that is not represented on the Xbox360. And MS tries to widen the market with games like Halo Wars or Banjo for example. The rest is up to 3rd parties. This is not MS or Sonys fault. 3rd parties want to play it save as it seems. Mirrors Edge was a try for EA and it flopped hard.
Imagine not having GamePass on your console...
