The T3i (600D) was a good camera in it's day.
But the 80D is a big step up in virtually every possible way!
First, you are going from a Rebel series to Canon mid-grade DSLR, which means a bigger, brighter viewfinder using a true pentaprism (versus a penta-mirror in the Rebel). You also will get a more rigid metal chassis and added sealing for weather resistance in the 80D. The 80D also has a higher specification shutter... with a faster top speed and flash sync, as well as rating for longer life expectancy. 80D also can shoot continuously at 7 frame per second (compared to 4 fps in T3i).
While both cameras are APS-C format (meaning, in part, that you can use any EF-S lenses you might have on both), the 80D is 24MP... or 33% higher resolution than the 18MP T3i. In addition to the newer sensor providing greater dynamic range and color you will also will find it more usable at higher ISOs... probably at least one stop's worth. Even with more resolution and faster frame rate, thanks to using the larger LP-E6N battery and greater power efficiency, you'll get about twice as many shots per battery charge with the 80D.
The 80D also introduced the 45-point AF system that Canon has been using in a number of cameras. First seen on the 80D, it's now also used in 6D Mark II, 77D and T7i. (In 80D and 6DII it has Micro Focus Adjustment feature, too... that's not provided in T7i or 77D). Your T3i has a pretty basic, but workable 9-point AF system, with one higher performance "cross type" point at the center, good to around -0.5 or -1 EV light levels and "f/5.6 limited". All 45 of the 80D's AF points are cross type, it's able to focus down to -3EV light levels (approx. moonlight) and is "f/8 capable" at up to 27 SF points. This last means that you can use a 1.4X teleconverter on an f/5.6 lens or a 2X on an f/4 lens. On T3i those lens & teleconverter combos would be unable to autofocus.
80D also has Dual Pixel AF in Live View (which was first intro'd on 70D and some form of which is now in almost all Canon interchangeable lens cameras). This is MUCH faster and more useful than the contrast detection AF your T3i uses.
There's a lot more.... Following gives you more detailed info about the 80D's AF system:
https://www.usa.canon.com/internet/portal/us/home/learn/education/topics/article/2018/July/Whats-New-45-point-AF-on-the-Canon-EOS-80D/Whats-New-45-point-AF-on-the-Canon-EOS-80DThe following are two very helpful, detailed reviews of all aspects of the 80D:
https://www.the-digital-picture.com/Reviews/Canon-EOS-80D.aspxhttps://www.imaging-resource.com/PRODS/canon-80d/canon-80dA.HTMAnd the following go into more detail comparing the 80D versus the T3i:
https://www.imaging-resource.com/cameras/canon/t3i/vs/canon/80d/ https://www.apotelyt.com/compare-camera/canon-t3i-vs-canon-80dhttps://cameradecision.com/compare/Canon-EOS-600D-vs-Canon-EOS-80DFinally, if you don't already have the lens, I'd highly recommend getting the 80D in kit with the EF-S 18-135mm IS
USM lens, which is usually the lens that's bundled with the camera. This is the latest and best of Canon's three 18-135s. It uses the new "Nano USM" focus drive, which according to Canon is just as quiet as STM focus drive, but 2X to 4X faster. It's a better all-around lens. It's also the only lens that can optionally be fitted with Canon's PZ-E1 Power Zoom module, which might be a nice accessory if you intend to shoot video. The EF-S 18-135mm IS USM normally sells for $600 new. When bought in kit with the 80D, you can get it for a lot less. (currently the lens in kit is half price: 80D body only is $999... or in kit with the 18-135mm it's $1299.)
The "better" standard zoom lenses are the EF-S 17-55mm f/2.8 IS USM (for it's larger aperture) or the EF-S 15-85mm IS USM (for it's wider angle capabilities). Neither is normally offered in kit with the camera, though, so they both end up more expensive.
P.S. I don't have either T3i or 80D personally. I have used various Canon with the same AF system as T3i and took about a quarter million shots over the course of five years with a pair of 7D that use the same 18MP sensor as T3i. I now mostly shoot with 7D Mark II, which are a step up from 80D in some respects (more sophisticated AF system, additional durability/sealing, faster frame rate), but might even be considered a step down in others (20MP instead of 24MP, fewer f/8 capable AF points).