I really like the 77D, but at the moment the pricing doesn't make sense. MSRP, they are very close in price because of the current Instant Rebate on the 80D. But that doesn't even tell the whole picture, because street price, body only, 80D is sub-$900 USD (for example, Amazon with fulfillment via Prime, which gives you free shipping and hassle-free 30 day return). And throw in a little bit more, and you can get a nice bundle with surprisingly useful extras.
There is almost nothing on it that's better than the 80D -- the Bluetooth is kind of cool, and I guess there's the DSLR-newb Guide UI, which some people have said is touch-friendly and cool, but I don't think either is a compelling reason to choose the camera. On the other hand the 80D is superior in a lot of things that often matter to people who buy midrange DSLR or semi-pro APS-C, like weather seal, pentaprism, battery life, and convenience features like more/better buttons, C1/C2.
The battery I think is a massively understated advantage of the 80D -- 80D uses LP-E6, which is a well-loved battery that's shared by many Canon cameras AND that you can get cheap third party copies of for the price of lunch at Starbucks. The 77D uses the same battery as the t6i/t6s, the LP-E17, which only has non-decoded batteries. That means either not knowing how much juice is left in spares, or paying $60 a battery for Canon originals.
So, just 2 spare batteries, and you're looking at an extra $100. If you have a grip plus 4 batteries (2 sets), that's a whopping $200 difference. And 3rd party LP-E6 batteries have gotten really good, as good as the original Canon ones.
The real winner in this round, I think, is the T7i. It's a massive improvement and an awesome hobbyist camera, a market where most of the 80D features are just not that important.
Keep in mind that I'd have a different opinion if it weren't for the current pricing strata. at MSRP $1200 versus MSRP $900, the 77D is a great choice. But at street price $880 vs $900 for the brand-new 70D, it's just a no brainer, IMHO.
I suppose the other argument would be for the new lens kit, but personally, I have zero interest in another 18-55 range lens, even if it's cheap and a little smaller. I'm not really sure there are that many people who want a $1000-range camera who don't have a kit 18-55 from a previous camera, or who have invested in a far superior alternative already (for me, that's the 17-55 2.8) .
I guess there could be unmentioned extras that would change the calculus too, for instance, really awesome wifi to desktop speeds for RAW shooting, but you'd think they'd advertise that if it were so.