I have the 70-200 f/2.8L non-IS and have previously owned the 70-200 f/4L for quite some time. I have noticed that both lenses at f/4 delivered the same exact image quality, which was, of course, stunning. However, if I had to pick a winner, it would be the f/4L as it did seem more consistent. Obviously when I go down to f/2.8, the comparison becomes pointless.
At the end of the day, the IQ among all three 70-200Ls is basically the same. Any leads are honestly highly insignificant. I wouldn't let IQ determine which of the lenses you would get. They're all fantastic.