The Canon 80d is a hobbist camera. By all accounts it is a pretty good one. Not particularly good at sports, and not for high end video.
The Nikon d500 is a pro grade camera. It is more rugged, better weather sealing, better auto-focus system. The video is ok, but it requires manual focus for moving subjects. Most professionals use manual focus for video so they can control DOF, specific focus point and so on.
Neither camera would be my choice for either of the things you said. For professional photography I would go with a Nikon d850 (if cost were not a problem) or a Nikon d750 if you wanted to save a little.
For video I would go with a Panasonic gh4 or gh5. I would also consider a Sony a7s II.
What I use is a Gh3 for event...