I have a funny feeling the high ISO NR settings were set differently on both cameras..I was thinking the same thing. I shot the 2nd and 3rd set of pictures in RAW so the JPG settings (like high ISO NR, sharpening, white balance, etc.) difference between the two cameras would not affect the outcome. RAW converted to highest resolution JPG in Canon Digital Photo Professional in batch mode (all settings the same).
The M should have the same IQ as a 650D since it's the same sensor..
The 6D being a FF camera should be better than the M..
If the in-camera settings were different, you've still got an issue (as the WB shows). DPP respects and applies the in-camera JPG settings, so unless you went in and actually changed all settings to be identical in DPP (which you didn't, at least not WB), you still don't have a good test. But at least all you need to do is go back and reprocess the RAWs.