All great points guys. As a former 5D Mk II owner and current 5D Mk III owner, they're great in low light. One other thing to add to the discussion is remember the lens matters too. Max ap lenses of f/4, f/2.8, f/1.2, etc. tend to focus faster, especially on the 1D Mk IV than narrower max ap lenses. Consider the 300mm f/4L lens on the 1DX vs. the 300mm f/2.8L on the same camera body. The latter will focus faster. Of course, stationary scenes who cares.
Had my 70-200 2.8II on the whole time. Great, fast combo.
I shot Wednesday outside with the 5D Mk III and 70-200L lens that you mention and it's hard to imagine a better combination. Oh the sharpness and color...............