That A7R image looks out of focus. If you were using Canon lenses on the A7R then that may be related to whatever adapter you're using. My A7R and even my NEX-7 have had some of the most reliable focusing of any camera I've owned.
I have the 5DMII which from what I understand the image quality isn't much different from the 5DMIII. My 5D image quality is great but my D800 or A7R are better especially with pushing shadows. All my work is in RAW so I haven't compared JPGs to see the differences.
Also, I've read a lot about shutter vibration and image quality issues on forums and that the 36MP+ sensor cameras require special handling. I've never found this to be my experience. I've gotten very sharp images with long 30+ second exposures even on an ultra compact MeFoto travel tripod using a 2 second delay or wireless remote. If there's any shutter shake I haven't seen anything that makes me think I should be concerned.
Next time try a supported Sony Zeiss or G lens and see what kind of results you get.