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I am using the Sony A7R with the lenses you mentioned above and with Metabones III adapter. In both cases the AF works fine, just a bit slower compared to the lenses each mounted on a Canon camera FF body. AF works on the full range of the 70-200 lens. The IS of the 70-200/4 IS lens works exactly the same as on my Canon 5D MkII body, I didn't observe any difference.
It's not terrible but I would say 'much' slower since it uses contrast-detection-based AF. In low light (low contrast) it's not very accurate either...
but hey, at least we have AF.
From my experience, it's faster and more accurate when choosing the Flexible Spot (Large) or "Center" Focus Area settings.
Also keep in mind that you can't use AF-C (Continuous AF mode with the Metabones)
I usually rely on EVF magnification to nail focus and it works quite well for static subjects when on a tripod.
The problem I am having is that when focus magnification (7x or 14x) is enabled, IS stops functioning and it's hard to stay steady at these magnifications. I have not found a workaround for this yet. If anyone know a trick for this, let me know.