That's easy, the 5D Mark III offers better image quality in video mode than the 6D with a VAF. The 6D downsamples the sensor using lineskipping and takes it down below 1080p, then scales it back up. The 5D will also produce better results and perform better in low light due to the pixel binning. The 5D Mark III can also record full 1080p RAW with Magic Lantern, the 6D is only capable of capturing around 720p.
For stills I feel that the 6D is the way to go, it has a great sensor that can outperform the one in the 5D.
Personally I would only consider a Canon camera for video if you plan on using the RAW feature with Magic Lantern, otherwise there are much better options out there. RAW with Magic Lantern isn't video, it creates RAW photograph stills at the desired framerate. H.264 on the other hand feels like standard definition, even when comparing the two on Youtube after the edit.