Coming from a Galaxy S8+. This is my first Note. I've read so much over the past few days that the Note 8 is basically a Galaxy S8++ but I would strongly disagree.
First, the design of the Note 8 is much better than the S8+. I didnt realize how rounded the S8+ was until I got the Note 8 in my hands. The Note 8 is much more comfortable to hold. The screen on the Note 8 is not as curved as the S8+ which makes a huge difference. I compared both displays next to each other and the Note 8 actually looks better. I was skeptical when I heard reviews that the display was better, but I did notice a difference and improvement on the Note 8.
Second, the Note 8 is much more responsive than the S8+. I will factor in that the Note 8 is brand new and the S8+ had been used since release, so I know I have the famous android slow-down that plagues any device. But I cant help but notice how much snappier the Note 8 is. Transitioning between apps is amazing. Animations are quicker. Texts send faster. Internet browsing is quicker. The overall experience of this phone is much better than the S8+. My last device was a Nexus 6p, rooted and custom rom'd, and I don't think I have/ever will use another phone that moved and responded as quick as my Nexus 6p, but the Note 8 seems to be almost as quick.
Last, typing. I am not sure what did it, but the S8+ was the worst phone I have ever typed on. I was using multiple keyboards to try to find one that would work. But it just never seemed to function like other devices I have used. I was constantly making errors. Typing never felt right. I was even having issues with autorcorrect, it never seemed to function properly. The typing experience on the Note 8 is MUCH MUCH better. Can't say enough good about it.
I know a lot of people have knocked those of us who have transitioned from a S8+ to the Note 8, but I have no regrets and would even suggest to those of you who can, upgrade to the Note 8.