Before I bought the Kemper I had the opportunity to actually try the Kemper and the AxeFX II. Both are brilliant units with incredible variety and lots of great options. However I got the Kemper because - at least to me - the sounds I got out of the Kemper were as close to the actual amp as possible. The sounds I got out of the Kemper were basicly the exact same as from the amps in that studio and that just blew my mind. The Axe however was very cool in the aspect of creating your very own personal sound even though it was a lot harder to get a sound I really liked out of the Axe (a brutal metal tone in my case). It took me about 15 minutes (with introduction of the kemper functions from a friend) to get a sound out of the kemper that I would use on stage right away. It took me about 3 hours (again - wit instructions of a friend about the functions) to get a sound that I "somehow" liked. I´m sure I would be able to get a killer tone out of the Axe too if I would have spent a few more hours on it.
I´m quite aware that this is absolutly subjective and should be viewed as it but for me the realism of the sound helped my decision a lot. Personally I think that the Axe II can´t compete with the Kemper when it comes to the realism of the sound and thats one of the many points that makes it such a great unit. I´d simply suggest you listen to a lot of clips of the kemper here in the forum and on youtube and soundcloud (just search for the tag "kemper" and you´ll see a lot of results) and do the same thing for the axe fx - and whichever you like more you should get