First - Besides being a sound engineer, producer, studio owner and guitarist, I am and always will be a tube guy! I own many different tube amps and cabs, mostly high-gain, as that is where my interest lies (Metal).
When that is said, I am absolutely sold on the AXE3. Like OP I am interested in how close the AXE3 gets to my real amps, but I approached this quite the other way around;
Now I physically own the amps and cabs I consider the ultimate setup for my band needs:
Engl Savage 120 + Mesa Boogie Mrk V 90watt
into
Engl Pro Cab 4x12" + Mesa Rectifier XL Cab
But it's not practical for me to bring these out on gigs, as they sit in my Studio-setup, so my aim was to recreate my dialled in sound on the respective amps and cabs in the AXE3.
Also I knew I would always want to play thru cabs for monitor needs live, either bringing along my own, or borrow/rental my way on fly in gigs and the like.
Therefore I knew I would also have to bring a power-amp always. For more "local" gigs and rehearsal I use my Marshall 9200 Tube Power Amp, with 5881 tubes - insanely heavy, but I care more for the sound, less for the practicality. (For others I will most likely use the Palmer Macht 402, have not come up yet.)
I started out with matching the AXE3 amp blocks of the respectable amps (Angle Severe 2 + USA Lead Mid Gain Bright) to my physical amps, one by one - using the 4CM described in the Fractal Wiki - flipping between the physical pre-amp and the Amp Block from within the AXE3 . Using the physical amps actual power-amp, I obviously turned off Power Amp Modeling in Global.
The results was mildly speaking flabbergasting...
With almost the same settings in both amps, staying on the Tone page, I came incredibly close real fast. Did they sound the same 1:1? No, just like 2 identical amps never sound the same, due to electronic component tolerance, tube-bias and wear and tear. But no doubt it was the same amps, behaving exactly the same way - and they felt and responded exactly the same when playing them thru their respectable cabs. Amazing! And you couldn't really say one sounded better than the other, just slightly different.
Remember, I was using the physical amps power section for this!
Next step:
Now the AXE3 out of Output3, before any Cab Block, into the Marshall 9200 Power Amp into first the Engl Pro 4x12" Cab, Switching speaker cable back and forth between the Engl Savage 120 output and The AXE/9200 to compare. And then into the Mesa Rectifier XL 4x12", switching between the AXE3/9200 and the Mesa Mrk V.
This was more tricky - I found that the Marshall 9200 was letting thru way more high frequencies than when going into the physical amps Power section, thru Effect Return. I slammed a Filter Block before Output3 and found I had to do Lowpass all the way down to between 4K to 5K, to match the 9200 to the Engl Savage. Almost same thing with the Mesa Mrk V. That helped big time! Again - not 1:1, but obviously the same amps and very close. And when I started to play around with Speaker Impedance Curves, different Tubes, Speaker Compression and a little deep tweaking, the result was INCREDIBLE!
I ended up with a result sounding SUPERIOR to my physical amps!! Even though I love those 2 amps, nothing isn't so good, you can't wish for it to be a little better, haha! - Well, on the AXE3 versions I had SO MANY MORE parameters to play with, and then of course I now was free to build the perfect true stereo setup, when combining the AXE3 various effects.
I was, and still am, blown away!!
The last step:
I am now in the process of adjusting my IR's and what comes out from Output1 (direct to FOH/IEM) to replicate in the PA what I hear coming thru my cabs. I have no doubt it's doable, and when I listen thru my Genelec 1030A's, it already sounds better than anything I've ever heard - on all volume levels btw. It will probably take a couple of shows on real PA's before it's perfected in that regard, but that's the easy part.
For my part, I am now convinced Cliff has cracked it! - To my experience the AXE3 is 100% there.
Good for you FRACTAL, and thank you!!
- And remember, the reason why we all think the AXE sounds so amazing, is because it sounds like tubes!