I also have both. The Axe FX 2 FW15 upgrade has allowed the creation of amps and cabs that rival Kempers profiles very nicely. There is more "realism" then I have heard in past versions of Axe Fx FW.
I find they both bring something different to the musical table. Since I have several guitars, I am very comfortable having several processors. I intend on keeping them both since I would find it extremely difficult trying to pick one to get rid of.
Cooper Carter does a great job of sharing great info and insight into what the Axe FX is capable of.He is a very talented guitarist who also is a good teacher.
https://www.youtube.com/user/SoloAWeek
I wish Kemper had someone similar. It really helps sell the unit.
This was my problem with the Axe FX II - with every new firmware upgrade everyone would rave about it and then another guy shows up on Youtube with a video with the AxeFX2 that sounds incredible. I was NEVER able to achieve those tones. I'm not blaming the AX - I blame myself. The thing is clearly capable of stellar tones and the effects were unbelievable, the tweaking options enormous, etc etc. I got sucked into tweaking hell and came out the other side not playing my guitar that much and not enjoying it anymore. When I got the KPA I loved the relative simplicity of it. For those who can access the secret sauce - the AX is great.