I am having trouble deciding which of the above cameras is right for my budget. It basically comes down to the question of how close the A7R with a stabilized lens comes to the A7II in terms of low light "EV"-gain, as in how much longer I can expose while handheld when comparing: A7 II + integrated stabilizer vs A7R + no stabilization vs A7R with stabilized lens. Also, does lens stabilization for adapted lenses work, that were made for different mounts than native FE-mount?
The official number if a 4.5 stop gain from the 5-axis image-stabilization system in the A7 II. This is the difference compared to having no stabilization.
For lens based stabilization, it varies and it is different for each lens. Expect 2 stops at least but there are lenses which claim 4 stops or so too.
The A7 II has built-in stabilization, so it works with all lenses, including adapted ones. With the A7R, adapted lenses extremely unlikely to work since adapters would need good communication between the camera and lens. Many adapters do not even have electric contacts which would be needed to power lens stabilization.
So to answer the final part of your question:
- A7 II vs A7 with unstabilized lens: 4.5 stops.
- A7 II vs A7 with stabilized lenses: 0 to 2.5 stops.
- A7 with unstabilized lens vs A7 with stabilized lenses: 2 to 4 stops.
Keep in mind that these are official numbers usually measured according to the CIPA standard. Your mileage will certainly vary. From experience, I rarely reach the numbers quoted. I don't consider myself shaky but it seems official numbers are based on best-case performance.