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In many action pictures, both are not up to the level of 1 series cameras. In many relatively slow pictures in AI servo, with additional center points activated, both can be surprisingly good.
The AF hardware module is the same. The 5DII has a significantly faster processor.
Here is one rare situation, where that processor difference is evident:
I was shooting in AI servo of flight (hovering) pictures of hummingbirds with extremely tight framing (300f4L IS with extension tube at 4.9'). At that close distance the slightest mis-focus is evident.
I pre-focused the lens, and waited for the bird to pop up above the feeder and look around. In perhaps 0.8 seconds, I had to find him in the tight frame, place the focus point on his gorget, acquire focus, have the mirror flip, and get the shot, before he darted back down to feed, or to fly off.
I tried that about 30 times with a 5D1, and it missed 30 times. I gave up and went to zone focusing.
I tried the same thing with 5DII, and it nailed the focus every time. People here on this board didn't believe that, when I showed pictures here about 1.5 years ago. So I showed 4 consecutive (not cherry picked) full frame shots, and the same 4 frames at 100% crops, showing that the focus was dead on. In one of the four pictures I showed, there were TWO ants on his beak (Keep in mind he is flying, not perching on a branch). In that 100% crop you can count 10 individual ant legs on his beak (because two of the 12 legs were behind other ant legs!!!
That said, 7D and 1 series are a better choice for action pictures.