As an ex Kemper owner and a brand new Axe Fx III owner (only 1 month), this is my perspective.
5 years ago I went through this very exercise of deciding which unit I wanted to get. The Kemper is a fantastic unit. It creates a fantastic profile of an amp and its very particular settings and set up at the time of profiling.
With that said, I decided to get a Kemper because certainly someone out there will profile an amp at the exact settings I like. (I was looking for a very specific boogie mark series tone). This is where the idea of profiles didn't work for me. Amps are very personal, and while I could find profiles in the ballpark of the tone I was craving, I could only find ones that were maybe 80-90% of the way there. Ok, well, that's fine. I will tweak and adjust as needed....well, this is where it sorta failed pretty hard for me. The more I would tweak these profiles, the more digital and synthetic they would start to feel and sound.
After several years of this, I decided that, even if I get caught in endless menus and tweaking hell with a "modeling" style amplifier, at least maybe I can get the actual tone I want, even if it requires hours and hours of tweaking. I sold the Kemper and bought the Axe. I had heard the Axe had best in class modelling and effects, so I figured I would try it out.
1 month in, and oh my.. I can't even begin to explain the giddiness of getting the tones I've been searching years for...and without the endless tweaking I was worried a modeler requires. This thing is absolutely fantastic. I've dialed in a better tone than I get out of my Boogie Mark V 25, and waaaaay better than the Kemper. Maybe 20 minutes to get that tone.
In short, I love this thing. So far, best choice I've made in my entire music career as a bedroom player. Huge respect for the team at fractal and their frequent updates. Only one month in, this unit has gotten better with fimware updates. I also want to give a shout out to Leon Todd. Check his YouTube vids. Helped me tremendously with dialing in some fantastic tones.