I would have to disagree.
The 80d has a newer sensor and auto focus system, higher dynamic range and has an articulating screen for video. The only real thing the 6d has is full frame and age.
The 6D is generally going to perform better for overall image quality (particularly where low-light is concerned) but the exception is video... the 80D has dual-pixel AF and the 6D does not. This means the 80D can do continuous autofocus during video and the 6D does not have that feature.
If video (and specifically video) were important to you, then that would be one reason to choose an 80D. For most other uses of "still" photography, the 6D will be the top performer.
The 7D II is heavily optimized for "action" photography. It has blazingly fast shooting speed, an amazing focus system, etc. and in most ways it is a "better" camera than an 80D. However... you specifically asked about stills and video. You would pay more for a 7D II but it sounds like you would not be taking advantage of the specific features that make the 7D II a high performance camera.