Here's my take on the Kemper vs Axe FX thing....
Now, first off, I don't even see the Kemper as a modeler at all, so comparing them doesn't make much sense to me. That's not a good, or bad thing, the Kemper just doesn't fit the definition of what I believe to be a modeler, so it's like comparing a delay to a drive pedal. They can both affect your tone, but not in any real competitive kind of way. The two concepts are just too different, and could easily be combined into a single rig. Several artists do this now, and even the Axe-FX has both concepts built in.
To me, a modeler is a device where a programmer replicates a software version of another device in a software environment as accurately as possible, where the end goal is to design every aspect, including tone, signal paths, and control behaviors, as close to the original as possible. A modeler can also go above and beyond the realms of physics and alter things that could not normally be changed in the real world equivalent without possible permanent damage to the original device. The weakness in this concept are the skills of the programmer, and the limitations of the technology being used.
For example. If you modeled a painting. The programmer would do his best to make it look exactly like the original painting from every angle, the 3D aspect of every brush stroke would be apparent even from a side view, and if they were going for pure accuracy, even the original artists mistakes would show up. If the Axe-FX was a painting modeler, you might even have deeper editing features that allowed you to alter the types of paints, canvas, colors and brush strokes used to make your own interpretation of the original work.
Now, I see the Kemper as more of a professional "sound camera" with no actual modeling going on. It doesn't actually model the amp, it more or less takes a snapshot of an amps tone at a single point in time with no deep knowledge of the internal workings of the amp. Now you can alter the tone to some extent, but this process is more like trying to use a set of general photoshop tools than actually reproducing the tone path of the amp. The real end goal with the Kemper is to get the best snapshot of the original without the need for any kind of tweaking. The weakness in this concept, is that you either have to have an army of amps, and tools, and skills required to capture what you want, or rely on someone in the community to have a similar ear, and the skills to capture the tone you want correctly, the first time.
For example. Back to the painting analogy. If you used the Kemper idea, as long as you, or the original person that captured the "snapshot" did a good job, the painting would look very real from one vantage point, but if you looked at it from another angle, the whole illusion MIGHT fall apart. You could run the work through a few different filters to alter some aspects, but on the whole the end goal is really to get the best shot of the original as possible without the need to alter settings. How good the final product is, though depends on a great many things.
Let me make it clear, I do not think either one is a better idea than the other. They both have their place. Like I said before, even the Axe-FX has this "snapshot" concept build in, because it's a great tool. If you have an army of amps that you want to clone, then you'd PROBABLY benefit more from the Kemper. However, if you don't own any amps, or you only have maybe one, or two you'd like to clone, then The Axe-FX might be more your thing.
Personally, I'm a very happy Axe-FXer, and I don't see any good reason to change. It already does more than what I want/need it to do, and it does those things very well, and to my amazement, it somehow keeps on getting even better. But I'm not everyone, so if you prefer the Kemper idea, then more power to ya. It's your gear, buy what makes you happy.
