So been trying out both 70-200s today. Been interesting.
The 2.8 allows a faster shutter speed obviously, but with the high ISO of the D750 the f4 is still decent enough in low light. For low light action the 2.8 is the winner.
As mentioned before, if it's outdoors or good light, it just depends if you want 2.8.
Focus speed is quick and snappy on both. Apparently the 2.8 is faster, but it's hard to measure when using one body!
2.8 is better built, but the f4 is by no means a cheap build. I would say it's a step up from say the build of the 24-120 f4.
Handling is subjective and will really depend on the person. With my previous injury the f4 is much easier. For someone with more strength I don't think it would be an issue. They may even prefer the thickness of the lens. The f4 is quite narrow in comparison.
Both have a great feeling zoom and focus ring. Could not fault either.
As for IQ, it's hard to tell without getting out and doing some proper shooting. Both look sharp and have good colours. Reviews have them as good as each other as far as I know.
The 2.8 is for me heavy, at nearly 2 times the weight of the f4, it really feels like a brick (to me). And makes the D750 look so tiny!
I'm going out at the weekend for a walk and some shooting. That will be the deciding factor for me. Sadly I am swaying towards the f4, but in a perfect world I would keep the 2.8 until I am fully fit. But this may not happen for a while and it would just be a waste.
Saying that, I might change my tune after the weekend!