I agree that the Axe isn't 100% there. Sometimes it's 90, sometimes it's 110. Clean compared to my Tone King Metropolitan, the TK takes it for sure. Playing live where I can't play as loud as I might like, it's often better than my tube stuff because I can get most of the quality of an amp plus pedals that's a lot louder than I'm actually playing without getting kicked out of a band or club.
I, too, like the rawness of a tube amp (and then I like taming it and/or accentuating it with pedals/pickups/volume and tone knobs). I found Scott P's thread on cabinet blending to be very useful in helping with that characteristic. I've tried tones of people's presets and while I respect the craft that goes into them, I don't use any of them because they sound too processed and non-dynamic mostly. I do just what Scott does, which is to say, amp and cab block and nothing else for the basic sound. Maybe a little verb. I'll add pedals to tweak the sound, but it all starts really basic.
I also love the repeat-ability factor of the Axe. Sometimes I plug my tube amps in somewhere and think "what's missing here?" Could be power source, tubes at a particular moment, planets unaligned or ?, but it just doesn't sound as good as I know it did last time.
I haven't sold my tube amps, but they sure get a lot less playing time since I got the II (they got more playing time when I had the Ultra). I don't find it offensive at all to say it doesn't sound just like whatever tube amp. I hear that in a bare room with nothing else happening. In a mix, live, I'm generally happy as can be and have lots of tube head guitarists with great gear come up and say they had no idea I was using a digital box until they saw it.
For me the Axe Ultra and particularly the II have gotten close enough that I committed to the path they're on, knowing it's only going to get better and better. I've spent 10's of thousands on guitar amps and for the ones I like, there are some that have gotten slightly better or more functionally useful (the TK Metropolitan is a great BFish meets Tweedish rig with power scaling), but the tube amps haven't improved remotely to the degree that the Axe has in the 3+ years I've been using it/them. If improvements continue apace, this discussion will likely become less and less relevant. In the meantime, I'm keeping some tube amps and pedals, and playing my II most of the time.
I like it when this kind of thread comes up. I think noting the deficiencies of the Axe helps it to get better so long as we don't pound them into the ground or say it's useless because it's not perfect.