Ok without adding more fuel to the fire, I feel I need to throw in my opinion as well.
I should start by saying that I've been an Axe-FX user for some time. I work as a salesman at a guitar shop where we sell/sold amp sims like Eleven Rack, Line 6 stuff and etc. I regularly use/test amp plugins for DAWs as well like EZmix, TSE x50, guitar rig, LePou plugins and etc.
I feel that all these products are and sound great. Again, personally I feel that some are better than others and that some are better priced as well.
Usually when people start discussing/arguing about Amp Sims and what sounds better, there are too many things to take into consideration such as personal taste, but we could probably write several more down.
Like hearing loss
Personally I cannot fathom why people think the Kemper "sounds better" than the Axe-FX II, I simply feel quite the opposite. But again, that is my own personal opinion reflected upon my personal taste.
I tried the Kemper and even tried making several profiles with it. I found it to not sound 100% or even 90% like the "real thing". It was close enough to sound good though.
I have A/B tested the Axe-FX II versus the real amp in a pro studio and I honestly couldn't hear the difference. I didn't even bother tonematching.
But before we take this flaming further, lets discuss the Kemper and Axe-FX and what they do.
Kemper:
The Kemper is a great tool for people who own amps/gear and want their own sound in a portable and affordable solution. They don't want too many dials to fiddle with and it just needs to sound great.
Well your in luck! That is what the Kemper will do, and it's cheaper than the Axe-FX II.
It profiles amp, cab and mic setups and you can download/buy others as well.
Axe-FX II:
The Axe-FX is for people who want to try out simulations of different brands of amps, pedals, cabinets and microphones. They can mix and match several Amp, Cab and Mic combination. Any sound they want to make out of nothing, they can do that with the Axe-FX. That is the key strength of the Axe-FX, you can do what ever you want and you have the processing power to do it. You can even tonematch if you want your own sound as well.
Now let's take a look at the hardware (correct me if I'm wrong)
Kemper (last time I checked) uses a 24 bit fixed point Motorola DSP processor. List price is about 12 USD per processor.
(Same processor are/have also been featured in products by Line 6 and Eleven Rack)
Axe-FX II uses two 32 bit floating point SHARC DSP processors. List price is about 300 USD per processor.
(that kinda explains the price difference eh?)
So the hardware dictates that it's impossible for the Kemper "to sound better" since it's using fixed point processing instead of floating point processing which gives a more preciese simulation of the "real thing"
SHARC DSP processors are also used by Universal Audio for their plugin suite. The plugins they make are reviewed to be almost identical to the real thing and are even better than the competition sim plugins.
Build quality wise, I don't feel any difference between Kemper and Axe-FX. Both are built to last.
I feel like that you probably lean more towards Kemper since it's cheaper and you want to model your own gear, that sounds like a great solution for you.
I think it's a bad time to buy a Kemper when brands like Line 6 are upgrading their amp sims with 32 bit floating point DSP processors. The new 500x series have a better DSP processor than the old 500 series, and it sounds awesome!
I'm guessing that Kemper will upgrade to 32 bit floating point. It's just a matter of time.
I love amp sims, and I love them all, not just Axe-FX II. Axe-FX just happen to be my favorite cause I can get any tone I want, I can load in my own cabinets, I can tonematch and I get amps and firmware upgrades for free! It's the best studio tool I ever bought.
I feel that the other amp sims like Line 6 and Eleven Rack have shitty Cabinet simulations. Great thing about Kemper is that you can make a profile of an awesome amp/cab setup, so not shitty Cab sim there. Of course in the Axe-FX you can load your own Hi-res cabinet IR file.
Well that was my personal opinion. Hope it helped.