It's more that that.
The aps-c cameras before the 80D had an ISO variant sensor, that means the sensitivity is not linear, has a cutoff point.
Other camera like Nikon, and Pentax had ISO invariant sensors for many generations meaning the sensitivity is linear and gives the same amount of noise pushed in post or with raised ISO. This makes the high ISO performance much better and normal PP work is much easier.
While the 80D is nowhere near the sensor performance of the Nikon D7000 or Pentax K-5II but is leaps ahead of the past Canon crop bodies, including the 7D MkII.
It is much preferable to switch to the 80D, anything below that is just a marginal difference.