Unreal Tournament - Hell if I recall correctly it used to be held as the gold standard for bots, I still boot up UT:2004 for a round against the bots every now and then.(UT:2004 of course being for the PC).
I know it's not for the 360, but just for fun, Tribes 2 has bots, they are quite good, their only problem being that they can't hop in vehicles(meaning you have a very unfair advantage).[Tribes 2 having been released as free-ware, and will run on damn near any PC, hell my old PC with a 2.00GHZ AMD CPU, 256 MB RAM and 32 MB vRAM {integrated} used to run it perfectly.]
I wish I could be of more help, but I haven't paid much attention to the 360 or the PS3 or the Wii for that matter, I have a perfectly fine PC and quite frankly, I never get control of the TV in my house.