The Kemper is kinda like a high-resolution copy machine that's good enough to print money. The AxeFx is more like an ultimate toolkit that's good enough to create money. Neither is "geared toward" any particular style or genre, but more toward a type of user. Either one is capable of modeling existing amps to where blind tests won't reveal the difference between the original and the copy, but the Kemper needs the original to do it, while the AxeFx gives you the capability of doing it without the original.
Most people are flabbergasted at how good these units are, but you'll read the occasional review where somebody gives up on or downgrades one or the other as "not quite there". There are a couple of reasons for that.
First, even originals don't always sound like originals. Due to age and/or component tolerances, not all amps sound alike. For example, I used to own a Marshall JCM 900 that everyone agreed was just magical. That model generally didn't sound as good as the one I had. On the other end of the scale, one of my brothers had a Fender Twin that was somewhat less than satisfying. What was happening was a manifestation of reality in that electronic components have tolerances that range from 1% to 20%, and there's a bell curve to that. Sometimes everything falls in place to form a natural born killer at one end of the curve, most of the time they're in the middle, occasionally you get a retard. Nothing wrong with either one of our amps, but mine was a "natural born killer" while his was... not so much. But if you used either of those as your baseline for comparison, a perfect copy of those models in general would have sounded "wrong".
The other difference is physical. A Fender Twin or [insert amp model here] has a physical configuration that affects its performance in a given environment. The Twin is two speakers built into a partially open-backed 20"x26"x10" plywood box with a heavy weight bolted into one of its long sides. Not only is that enclosure going to affect its sound, it's going to affect the way the sound is projected from it. Most of the sound will come from the front, but some will come out the back out of phase and bounce off the rear wall (or whatever it hits first, plus subsequent reverberations). This is the much-discussed "amp in the room" sound that modelers in and of themselves can't possibly reproduce. As a result, all modelers from a $200 bargain basement pedal to the AxeFx Super Deluxe Ultimate Platinum Edition X often sound like anywhere from bad to perfect recordings of what they're modeling.
So, which is better? It depends on the user. Either one will probably get you where you need to be. The Kemper sounds great and is easy to deal with. The AxeFx sounds great but is dramatically more configurable, to the point where you can create amps that don't currently exist. It also has more and better SFX than anything on the market. The downside to the AxeFx (if you can call it that) for some people is you can do damn near anything, which leads some people into analysis paralysis. They start tweaking parameters endlessly and are always wondering if there isn't something more they could do to make it better. People complain that they spend more time tweaking than playing. Not that they need to, but just because they can. The thing has numerous adjustments you can make where you won't even know what the hell they are, let alone what they do, and many of them interact.
Personally, I'm of the "rather have it and not need it than need it and not have it" school of tools and feature sets that let me do whatever the hell I want, so the AxeFx suits me. If you just want a huge pile of amps/effects to play with, the Kemper might be the better choice.
