I currently own a DSG MK7 GTI and my SO has a 2020 BRZ. I was looking at a MK8 GTI SE or a MK8R but decided to order a GR86 instead.
The GTI is an excellent all around car if you use the practicality. You can fit an outrageous amount of stuff in them, they are quiet and comfy, get 35mpg highway, and are fun and flickable when you take them on a backroad. I've taken mine on 2000 mile road trips, 15+ track days, to the snow, in elevation, you name it. Never has faltered. The DSG is an excellent transmission, manuals are a bit flimsy and numb but if that's your preference it can be helped. My personal opinion of the negativity surrounding the haptic controls is that it's overblown. I played around with a MK8 at a dealership and found the infotainment easy to navigate through and didn't find the buttons overly sensitive - they took a solid touch to activate and clicked in. It wasn't pure touchscreen. I tried rolling my palms onto them to see if it would accidentally activate but they did not. Materials wise - from the drivers seat it felt the same as my MK7, but definitely feels very modern with the big wraparound screen. I was quite happy with it. Others seem to have had worse experiences but IMO a lot of people who hate on it haven't actually experienced it yet, and the owners I've talked to have said nothing but good things about the car.
If you plan on tracking the car, get the 86. I've built up my MK7 to be a pretty capable track car and go to the track about 10 times a year. Even though it is pretty fast (330whp, 1:44 at Laguna Seca last time out) it is not the most engaging thing to drive. I've autocrossed our BRZ before and it just feels so much more connected, and that was bone stock. I am switching to an 86 because I don't find myself using the practicality the GTI offers that often, and want to own something a bit more sporty before potentially having kids in the next few years. I see the 86 as a far better platform to both learn as a driver and build for track use. I also have the luxury of being able to bike to work and only occasionally having to fit my 35lb dog in the back seats, so the practicality is something I can sacrifice.
If the car is going to just be a daily and weekend canyon carver, the GTI is really tough to beat. The MK8 has been praised as dynamically better than the MK7, and the MK7 was already pretty good. I can see myself switching back to a MK8 R in three or four years, especially if they do a mid-cycle refresh and address some of the interior deficiencies. The GTI is far easier to simply maneuver around and live with day to day. Easier to get in and out of, quieter, far better visibility, better MPG, more comfy. But for fun, the BRZ (and I suspect the 86 will be the same) is far more engaging and fun, even if its slower.