On test charts, the 70-200/2.8L IS II will have a very slight advantage in the situation you describe. In real-world shooting, likely no discernible difference in that scenario.
The real issue isn't IQ, it's if you need that 1/1000 s and can only get to 1/500 s as high as you're willing to push the ISO, or need shallower DoF for portraits.
The difference between f/2.8 II and f/4? $1000. The difference between needing
an extra stop and not having it? Priceless.