When you look at the charts below you'll see that they're very similar in terms of noise up until about 6400 ISO. After that it appears the 80D is getting overly soft and saturates the reds and blacks more.
I also compared the dynamic range of these two cameras where I found the 80D showed significant improvement over the 70D. You can check that out HERE
To understand the methodology of my low light testing which will be included in the upcoming comparison CLICK HERE
If you own the 70D and want to learn all about your camera the fastest and easiest way possible check out my Canon 70D Crash Course Training Tutorial HERE
The 80D Crash Course is now available CLICK HERE
Keep checking the blog for more great lessons, shootouts, and comparisons!