Both have an APS-C sized sensor, which is large albeit not as big as the full-frame unit in the EOS 5D Mark III camera (which I thought was great).
The 80D has higher resolution (24.2 megapixel versus 20.2 for the 7D Mk II) and a variable angle touch screen that you use for focusing, and Wi-Fi connectivity and near-field communications - there's a free, and OK-ish Canon app for Apple iOS for remote shooting and file transfers. Plus the auto-focus, while not as superfast and accurate as on the 7D Mk II, is excellent.
While I never got to try out the the Canon EOS 70D, I did have a go with the 7D Mk II a while ago. On balance, I think Canon made a better general purpose DSLR in the 80D than the 7D Mk II.
Image quality is great: I've been lusting after pricey full-frame cameras, but the 80D, which retails for around two grand for body and kit zoom made me think I could get away with spending less, yet get very good results. The new sensor in the 80D and surrounding technology is also quite forgiving when taking pictures, and I got several good ones in situations where my 7D would've let me down. And, it's about a thousand dollars cheaper than the newer 7D Mk II.
I did use very good lenses including the Canon 70-200mm f/2.8 and my Sigma 35mm f/1.4 most of the time, but the 18-135mm f/3.5-f/5.6 kit zoom for the 80D with image stabilisation and "nano" ultrasonic motor is quite good and sharp too. The lens can also be used with an optional power zoom adapter, and microphones can be mounted on the hot shoe on top of the 80D - great for videographers.
While you get very good 1080p at up to 60 frames per second video with the 80D, there is mysteriously enough no 4K support.
This could be a deal breaker for some, and I'm surprised Canon didn't manage to squeeze it in, since so many competitors offer 4K, albeit with varying quality.
Despite the lack of 4K video, the 80D is a nicely rounded camera that's worth checking out for Canon upgraders not ready to give up on their DSLRs.
Update for Huawei Mate 8 review
Speaking of phones and cameras: when I tried out the Huawei Mate 8, I thought the image quality for both stills and videos was disappointing, despite a hi-tech 16 megapixel Sony sensor.
Turns out that my review device had buggy firmware. Huawei flashed the Mate 8 with new firmware, which helped image quality heaps. The version I have is NXT-L09C183B130; parallel imported devices are likely to have different versions of the firmware, but Huawei told me all will have the release software for the camera.