I had the Axe II for a year. It's a good box, but I honestly could never use it direct for "large" productions, only pre productions. I always preferred mic'ing a real amp (I don't do metal. Mostly pop, rock, country, bluesy, soulish etc) I noticed the Kemper, but thought it looked funny. Some 3 months ago I got to borrow a Kemper for a few days to check out...it literally took me 5 minutes to put my Axe up for sale. Honestly. At last I had the clear, raunchy yet very pleasant saturation I longed for. The same attack, dynamic reaction and bloom I'm familiar with from my tube amps.
Obviously, your ears only can decide what you need! And if you need all the routing and amount of efx the Axe provides, you won't be able to do all that in the Kemper. It's sufficient for me though, and the most important part to me is the amp modeling anyway.
There are way more parameters available to tweak on the amps in the Axe, but I still wouldn't say that amp sounds could be tweaked less in the Kemper. It has some VERY effective parameters that lets you tweak a profile into most anything. The parameters are made to alter the character in very musical and sensible ways. To me, much more so than using real amp component values. The Kemper is also much easier to tweak due to parameters being directly accessible, or just a click away. You can even adjust several at the same time with all the dials available.
Obviously, this forum will prefer the Kemper over the Axe Still, I'm not a fanboy of any equipment, and my choice is based on my ears and professional use only! If I find something that sounds or suits me even better, I'd switch in a heartbeat