This is just my opinion on it, some may disagree but opinions are like assholes everybody has one. Plus I spent enough money on the damn thing and own "real" tube amps\cabs and my hearing is pretty good so it's not like I'm talking out of my ass, but take this with a grain of salt if your looking to snag an Axe or want to know the gritty pro's con's of this thing, which ultimately there are very few con's.
It sounds great - first and foremost. Better than any VST or Amp sim out of the box. I've gotten similar sounds on my Computer, if not better - but it requires CPU Usage and it's never real-time, always during the mixing stage. The Axe is real-time, these tones are ZERO LATENCY that you just can't get with these other VST Plugins\Products, especially if your a Reverb\Delay\EQ Slut like me.
As far as criticism, I do notice a lack of clarity and definition which is probably because Cab emulation is not 100% there yet, IMO. There's just a certain level of resolution\clarity in the higher frequencies you just don't hear and are actually rather harsh when compared to sitting in front of a real tube amp and nice cab. I've been through hundreds if not thousands of Cab IR's and although some are nicer than others they really aren't the real thing. They all end up sounding like a thin sheet is covering the speakers. Perhaps a lot of these older folk can't hear it due to all the concerts and what-not, but I've had a number of people listen to it and the first thing they notice is that it doesn't sound as "clear" as a real amp and cab, and anybody who wants to argue that fact should get their hearing checked. I've compared this thing on Yamaha HS80m's, EV's, Bose Headphones and Mackies so far and I always hear a lack in clarity and even a harshness that I don't get if I just turn my damn amp on and play it through my cab. The real thing is smoother, harmonics are clearer, there's a higher resolution\clarity that I don't hear in ANY modeler. That is my true one and only gripe about emulation. So, does it kill the experience? --- Fuck no. Please read on.
Taking what I've said into consideration, when you MIC a real tube amp you lose a lot of that Clarity anyway. The EQ Curve of the MIC you are using cuts a lot of the clarity out and you end up going into a digital board 9/10 regardless. When mixing you cut even more of it out to make room for Vocals\Drums and other instruments which leads me to what I ultimately feel the Axe is best suited for if your not running it into a Tube Power amp and real Cabs or FRFR Speakers: Recording.
The Axe almost perfectly emulates the end result of MIC'ing an Amp Cab and hearing it through Studio Monitors. If you MIC a Real Amp and run them A/B and you are sitting in a Studio Booth you will probably not notice a difference. You will notice even less of a difference in a mix. I would argue that 99.99% of the human population would have no fucking clue it's not a "real tube amp". Where it really shines is the fact you can have 2 Amps, two Cabs, and all of the effects consolidated into 1 Unit emulating the entire effects & recording chain which in an analog environment with traditional hardware might cost tens of thousands of dollars. It's not that it only sounds good, but that it also emulates the entire effects chain perfectly every time and saves HOURS of work with ZERO Latency. It's fucking amazing.
So, I'd say it's 95% there in terms of sonic comparison, and that's an opinion anyway, most people can't hear a difference. I'm a whiny bitch and I absolutely hear some clarity\high frequency issues and slight harshness that all sims have that most people cut out of the mix and cover up with other instruments. I only notice because I play without any backing tracks most the time and you'll start to pick up these issues after many hours of use. I hope digital emulation will overcome this some day but for the most part it sounds amazing. If you are playing along with CD's or jamming in a Band it sounds amazinger. My profile picture was taken when I was using the 4 cable method and that lasted a few days, I'm now back to using the Axe all by itself because it sounds better than trying to MIC the Cab which can be rather difficult if you don't have a nice Studio and treated rooms.
Anyway, hope that helps.
-Justin