Personally, I think if you're looking for maximum tweakability and extreme creativity in terms of building presets the Axe II may be more up your alley. The Kemper offers plenty of tweakability, but doesn't offer nearly as many advanced parameters.
The Axe is more of a "build your tone from the ground up" type of thing. The Kemper is completely different. It's more like "capture the tone of your existing real-life rig or someone else's" .
Some people see the smaller amount of tweakable parameters within the KPA as a negative. I disagree. I find that the KPA is immensely easier to use and it's much faster to dial in a usable tone. There's so many advanced editing options available with the Axe that creating your tones becomes a hobby in itself. I've spent way more time playing and recording since I've gotten the Kemper (I owned the Axe II for about 18 months). IMO, all those parameters just aren't necessary with the Kemper. If a profile doesn't work for you, maybe tweak a little (some EQ adjustments), but other than that I say just move on to another one that may suit your needs better. There are thousands of profiles available covering hundreds of different amps.
I fully understand when people say they prefer the Axe because they need tons of effects, advanced routing options, like the idea of building their own tone from the ground up, etc.
When people say that they prefer the Axe's raw amp/cab tone, I find myself scratching my head. I just don't get it (unless I know they're aiming for a tone that's not really possible in real life- an artificial tone). 99% of the time, the KPA sounds just like the original amp and cab miced up. With the Kemper, the sound coming through my monitors sounds like it's coming directly from a miced up amp/cab in an isolation room. The Axe just sounds like a really good digital model of a real amp.