I own both the Kemper and the AX8. The comparison above is 100% correct. My biggest disappointment with the Kemper was that the profiles could not be tweaked like you can tweak a real amp, thus, the never ending search for a profile that sounds like the sound in your head (it can be a difficult search, the quality of profiles available varies dramatically). If you own a bunch of great gear, you can profile that and have your full selection of sounds available, BUT you need to profile the amps at all of your used settings, even as far as with your overdrive pedals, since the Kemper dirt models leave a lot to be desired IMHO. This also depends on your skill in recording, mike placement, and recording gear, thus the huge market for professionally recorded profiles.
On the other hand, with my AX8, the models sound and work like the amps should. The experience of setting up your own sound, or any sound you can think of is much more rewarding within the confines of the box. It works very well with any setup you can throw it into, the ease of cab IR implementation is fantastic, the the modeled EFX are excellent. I play it all the time and the Kemper is only brought out occasionally for recording. I have a few profiles that I use for that, and they are excellent.
The AX8 is a better unit for someone who knows how to get a good tone on a proper amp. The Kemper is a great for what it does, but you must either find a profile that sounds the way you like it (or very close to it) or profile and load your own gear into it. It is excellent for that use.