I've had my unlocked Note 8 for over a week now and couldn't be happier.
I had an S7 edge before and I hated it, wish I had never traded in my Note 4 for it. Within the first 30 days the rear camera glass shattered due to the phone overheating (I was driving, using google maps, charging, and playing music). Even now, just booting up the S7 Edge would cause the whole phone to heat up considerably. With the Note 8, I have been using Moonlight (PC game streaming) and playing games like XCOM: Enemy Within and TItan Quest and the phone remains so cool to the touch that it amazes me. I've gone so far as to loop 3DMark benchmarks just to see if I can get the phone to heat up and it never did.
I don't know if its the SD835 or the extra RAM or both but everything is so smooth. My S7 Edge had trouble backing out of youtube while a video was playing, often hanging on the main page before finally quiting. The Note 8 doesn't give a shit about anything I've thrown at it.
The battery life has been amazing too. Just yesterday I was replacing struts, brakes, and doing a tune up on my car and had my phone pumping out tunes while I worked. I ran it for about 7 hours (Headphone out to AUX in on my car) and it only dropped 11%. I tested the battery usage with Moonlight and about an hour of play only took about 15%. With my S7 Edge, I could read GAF for 5 minutes and it would drop 5%.
Oh, and the screen quality is amazing. Direct sun light viewing is just as good as indoor viewing. The screen on my Note 8 seems a bit warmer than that of my S7 Edge but its nothing that can't be corrected since Samsung was nice enough to offer more control over the display color balance. Heck, there are RGB sliders that allow even more control. My only gripe is the terribly high response time of the display. Ghosting is a serious issue, mostly on black scenes, but that's just how AMOLED displays are.
The dual OIS cameras are great but I wish they'd start packing 16MP cameras again. My old Note 4 took some amazing pictures and my S7 Edge took some decent pictures, shattered camera glass aside. The Note 8 takes some amazing pictures thanks to the software but I want to take better 16:9 pictures without having to sacrifice image quality.
Overall, I love the Note 8. I wish, same as anyone else, the battery could be larger but I understand Samsung playing it safe after the Note 7 meltdown. Hopefully, with the Note 9 they go back to taking chances on new features again.