Personally i like 5D2 in camera JPEG sharpening method rather than 6D, but luckily i often use RAW file, so i can manage my own sharpening method.
The 5d2 has the sharpest sensor output, esp. at lower iso, of the 5d2/5d3/6d generations, so it can do with less in-camera postprocessing. The 6d is at the other end of the scale, it trades some sharpness for higher iso capability - to compensate, Canon obviously has implemented more aggressive sharpening. I don't think you can do anything about this except bug Canon for a fw update.
I remember this issue being discussed when the first 6d raw and jpeg samples were out. This is more or less the difference between the "pro" 5d2 and the 6d which is tuned for sooc amateur shots, Canon has to protect their 5d3 after all :-o
Btw. the difference between your sample shots is really larger than I'd have expected it, maybe some other problem is at work here in combination with the above sensor difference.