If you will be taking pictures of things that move, the D500 is certainly better than the D7200. I have both. The focusing system is much better in the D500. Also, the focus points are spread all the way across the screen. That can be very helpful.
Other things that make the D500 a better overall camera in my opinion:
Construction, it's much beefier and weather proofed.
Bigger, brighter viewfinder
Auto AF fine tune. Some people like this, some don't.
Articulating touch screen - this can be great with live view, and makes things like picture review easier.
Focus point joy stick.
Button lighting for nighttime work
Huge buffer for shooting continuous frames, and 10 frames per second. This is a really big deal for those of us who shoot sports and wildlife. You may not need it often, but when you do it is the difference between getting all the action or not.
Dedicated back button focus button.
While some will tell you otherwise, it has been my experience that battery life is longer. Other users have reported short battery life, but often that is due to settings that can easily be changed, or using inferior batteries.
I never shoot video, so I won't comment, there.
All in all, if the money is there, I would always pick the D500 over the D7200.
With that said, though, I love my D7200 and still use it all the time. I would never consider it anything but a great camera. I use it as my wildlife backup and my primary landscape camera.
Also, I've never shot a D3400, but if you can identify all the features that you feel are missing, that might help you with you decision, as well.