No, profiles made originally sound exactly the same. The profiling process has improved, but the profiles don't change how they sound, they're two different things.
Every time the AxeFX gets an update you have to adjust your settings and sometimes you can't get it totally back to where it was.
Constant updates are a double edged sword for both the user and the product.
The other aspect is how many updates are needed. The Kemper hasn't really needed any updates to get to sound the way it does today. Because of the way Fractal constantly change the models and tech then the Axe really has needed all it's updates to get to the point it's at today.
It's a different concept and ethos. But it does underly that the Kemper got it right and the Axe (and others) have spent all this time still trying to catch up to the Kemper. The thing that a few studio owners have mentioned is that for them most people use the Axe for its tremendous FX and not its sim, while the Kemper is used for its sim. To me that speaks about the strengths of both.
The real trouble for both units is competition. Less so for the Kemper because of the patent although they don't seem to have defended it against Mooer (or maybe they're not aware of that), for the AxeFX though there have been a myriad of other standard sims that have come out, each cheaper, each pushing the envelope that little bit further. Companies like Yamaha are able to undercut and mass produce. Software options don't have to worry about the overhead of hardware at all.
I get the feeling that Christoph's point about the Kemper was more that it's at the limit of signal emulation. I seem to recall him saying something like "it can't get realer than this" in terms of that there is almost nothing differentiating the result of real vs modeled in terms of waveform itself and the whole "guitar amp" nut has been cracked. Now I'm not sure if I truly believe that myself but it does feel like there hasn't been anything that's come along and sounded more like a real amp yet and the steps that others have taken have been getting smaller and smaller.
I do think there's still room for improvement in the profiling process and in the cab (which should have some room reverb and maybe a higher resolution), and I actually wish that the background loops were optionally stored as part of the profiles because that noise even just as a frequency graph to apply to white noise because that aspect totally changes the way a profile sounds/feels once you switch off from profiling mode.
Anyhow, my experience of both communities is that there's good and bad, overall to me the FAS one feels more aggressive and defensive, but thankfully both have calmed down a bit in recent years and got back on with making music.