I own both and, in my opinion, one of the big advantages the Axe-Fx has over the Kemper is having complete and authentic control over the tone stack(and other parameters). The Axe-Fx is infinitely more flexible, no question. Personally, I don't hear the "sameness" some people mention regarding the KPA's amps, but that's me. I own both for a reason, though. There are amps available for the KPA that haven't been modeled in the Axe... yet anyway.
For me though, I love that the amp controls react realistically. Having said that, while the KPA's tone controls don't react like the knobs on the actual amp for a given profile, I do find them to be extremely powerful and musical, and lend quite a lot of sonic versatility, though not remotely in the same league as the Axe-Fx.
As far as realism, they both sound exceptional. It's just, in addition to parameters that react just like the controls of the amps they're based on, there are a lot of outstanding features that the Kemper simply doesn't have, and at the end of the day, the sheer versatility and flexibility of the Axe gives the end-user the ability to create (and recreate) virtually any tone they can imagine or have heard.