Which one should I choose? Canon EOS 80D or Canon EOS 77D?
For me, it would be between IS during video and bluetooth from the 77D vs. larger sensor area, faster maximum shutter speed, longer lasting battery, larger viewfinder coverage, faster fps, weather-sealing and an actual pentaprism (not pentamirror) for the 80D. I would go for the latter, the 80D.
Sometimes buying last year's model may save some money. I suggest reading the full specs side by side.