i own the 2 machine at home, the Kemper isn't superior to the Axe II, he's essentially less expensive, easier to set up and give very close results. Then, it's 2 different concept, the Axe is an amp simulator, the Kemper take a "picture" of a particular amp setting and gives you some options to play around.
The Kemper bandwith seems more restricted (lack of sparkle highs), yet, it's not usable for live set (midi bugs...). If you play it on a real guitar cab (and desactivate the speaker simulation) the results are ok, but not fantastic (compared to cheaper solution). The solution to avoid this is to make a profile with just a load box and no guitar cab, then when you use a guitare cab, it's much better and natural sounding. Whatever, I have some doubt if you have to face a real amp on a gig that you will be really "hear-able" due to the sound signature of the Kemper. So... different machines
Today, if i have to take one for a live gig, it's the AXE II. i've been very septical about Axe II, because i didn't hear much difference with my previous ultra (played at home and live). I ordered it just to give it a try and finally, it stays at home. I was more expecting from the Kemper, and on some point, the kemper is a little bit disapointing, but as it's the beginning and many things still have to be tested/added/done, it deserve a chance.
The Kemper is a fantastic tool for home studio, gives exellent results for jazz, blues, pop, rock, hard rock but if you're going in faster stuff you may notice that there's something strange.
There's something wrong in the attack when fast playing soloing, kind of latency, lack of punch, i don't know exactly, but it's not like a real amp. The axe is much better on that point.
Whatever, the Kemper, is a good investment, effects are cool, it sounds very "musical" and until your are not a shred/speed/metal/trash exclusive guy, you will find what you're looking for, and most of all, it's easy.
The Kemper seems to prefer guitars with moderate output level.
PS : i'm a very critical guy, so if you think my post is negative, no it's not... just that my job is to detects what's wrong on product so i use to spend more time on what's negative than positive.