I have an Axe III and REALLY dig it, so take this with a grain of salt.
IMO, the Axe III has literally raised the bar for modeling and options, AGAIN.
I also have an AX8 and LOVE that thing. Great piece of kit, not going anywhere.
However, the Axe III is in a class by itself and FAR away from any others as far as I can tell.
What I see as BIG improvements are in the interface, options, flexibility, and just HUGE processing power.
Obviously you can still create presets that will MAX out the processor, yet it's really not necessary.
Multiple outputs, multiple channels on EACH effect, amp, and cab, and another leap in modeling algorithm.
One drawback, if it is a drawback, is the proprietary foot controller(s) are not yet available.
So, you will need to use something else for switching if you want to use it live and be able to switch things.
That said, many peeps seem to have some kind of midi foot controller and the Axe III is controllable that way.
Fully assignable functionality, meaning you can assign things (whatever parameters you'd like to be able to switch), they are not set for you.
I used it at a couple theater shows 2 weekends ago, first time out. It went very well.
It is also 3 spaces, not 2 as the previous Axe FX II XL+.
I have to fly to gigs this weekend, so it's AX8 for this trip. Hope to have the Axe III ready to travel soon.
I'll be hanging on to both for versatility and flexibility. And backup.
If you're on the fence and haven't tried an Axe III, it's a pretty amazing unit. I'd certainly give it a shot...
Caveat: You'll need to spend some time with it to get the hang of setting things up, yet it's a very capable machine and tones are pretty stellar right out of the box. Of course you CAN tweak like a maniac, however it's not necessary. Although, I keep learning new tricks and that can really open new doors. There's lots of guys that are willing to help if you need it. Not Fractal employees necessarily, just other users and players with ideas, tips, tricks, and sharing whole presets, individual blocks, even IR's.
Last thing for now, remember it's not only a direct output unit. You have many options and the 4 outputs allow for you to tailor those options. Point being, you may enjoy it direct to PA or computer, feed studio monitors, go into a power amp and cab, and/or you may want a feed to your in-ears with specific EQ and effects, etc...it's all possible.
Best of luck. It's a great time to be playing
Oh, BTW, I have a Kemper as well and they are great units for sure, yet more of an amp snapshot. Great if that's your need and/or preference. I like being able to profile MY heads, cabs, etc and have MY sounds. Kemper also has some great profiles available.