I have both. They kind of complement each other as they each have unique strengths and weaknesses. Some of the major points that stand out to me are:
80D
-DPAF - This is awesome. Super accurate live view focus and AF during video
-Screen - Articulating touch screen. Great for shooting from awkward positions. Touch AF is pretty handy.
-Dynamic range - Better than 5D3 at low ISO. The 5D3 catches up by about ISO 320.
-1080 60P Video
-Wifi - Can be controlled remotely via phone or tablet
-Anti-flicker - Gives your more flexibility when shooting under fluorescent lighting
5D3
-Larger sensor - Get that sweet 35mm image look with wide/normal range primes
-Better high ISO IQ (in terms of both noise and DR)
-AF- 61 points vs 45, additional customization options, spot AF mode
-Ergonomics - The 8 way multi-controller and full size thumb wheel offer superior ergonimics imho
-Can record clean HDMI out
-Dual card slots - Versatility/reliability, particularly useful when shooting events
Overall, the 5D3 is my workhorse camera, and it is simply an outstanding tool that can handle nearly any job. The 80D is very versatile in it's own right and brings some exciting new technology that enables unique creative possibilities.
If I'm going to do a paid job, I almost always use the 5D3 as my main camera. If I'm going to shoot some photos of my 6 month old (not an unimportant task by any means), I'll often grab the lighter 80D and pair it with the 35IS. This makes for a very manageable package that allows me to experience the moment and not worry so much about my big heavy bag of gear.