Also, I notice they list Petrucci as an artist. I had a look on stage at his rig last tour (fortunate to do so, was I) and I am sure it was entirely Mesa Rectifier MIDI enabled preamps and Mesa Simul-Class2:Ninety rigs for the amplification, ran to two small 12" (or 10") cabs miked up offstage (so less bleed from live drums, more control over the sound) so I am curious where he actually uses this in his signal chain? I doubt he actually uses it for anything other than effects??? Same for Myung - he was using a DI box and a Demeter power amp ran on a dummy load for overdrive. (I chatted with the bass tech, friendly guy! The entire crew were friendly!)
Can't find any more recent info. Pretty sure Petrucci does the same thing, with Axe-Fx as effects processor rather than amp modeler. Don't know about Metallica.
There are quite a few artists who do use the Axe-Fx or Kemper live in lieu of amps though: Animals as Leaders, Periphery, Paul Masvidal from Cynic, Devin Townsend (sometimes, he seems to switch back and forth a lot), Jeff Loomis in Arch Enemy uses a Kemper live (https://www.youtube.com/watch?v=J92RP-fFO_g). Plus quite a few lesser known musicians. If you have an Axe-Fx, you can do a fly-in gig with it and have a consistent sound without being at the mercy of whatever crappy backline the venue has. Handy tool for a guitarist for hire.
Especially in metal though, there's a certain showmanship aspect to having a bunch of big loud amps on stage. A lot of the bigger bands for years have even lined stages with dummy stacks of 4x12 cabinets just for show. So even if they start using a modeler, they probably won't make a big deal of it. Smaller bands, playing in smaller venues run into the problem of stage monitoring. You can run your Axe-Fx into front-of-house and probably get a good sound to the crowd, but a lot of the smaller venues have lousy monitoring setups on stage and guitarists are used to essentially using their amp to compensate for that. So you might still want a power amp and cabinet on stage in that case.
Anyway, I have an Axe-Fx II and it's replaced all my tube gear. I wouldn't say it sounds 100% the same, but it's really close. Beyond the sound, what it does that other modelers have not done so well is get the "feel" of playing through a tube amp. The really subtle dynamics and compression that you don't necessarily hear but that affect how you play when your ears and hands are reacting to what the amp does. Leaps and bounds better than Line6 or Podfarm. And at apartment-safe volume levels, I'd even argue that it sounds better than most tube amps, so that's a huge plus for me.
From what I've seen on youtube of setup run throughs, people almost always have a complete non-fractal set of equipment for backup, but an axe-fx patch can actually contain all of this equipment. Manufacturers even sell their own racks that can be loaded into axe-fx.
Even the guitar amp simulators in apps like Logic Pro X sound pretty ropey. My friend (who is an excellent guitarist and teaches many many people) struggled to get a good sound out of it, and I really did as guitar amps are completely alien to me (why a presence control eh? why not just leave it on 10 and let the treble do the job???). To be fair to the developers of the software based ones, they make a good attempt but amp simulators never ever sound like the real things.
In my defence I used to use them for a while as a bass player but now am entirely analogue, with real glowing warm things in my gear. The difference is like chalk and cheese. I confess I always valves in the preamp stages - I do have one that uses an EL84 (normally a power amp valve) in the preamp stage combined with a 12AX7 for a great round sound; I used class D for the power amp because I don't want my back to break carrying gear). I have played for 20+ years and my ability these nuances has improved, so I wouldn't have heard the difference to begin with, that's for sure. Pity my ears have been subjected to drummers in that time, or I would hear the differences far better!
The hardware valve sound is a mix of compression, microphony, and at least two different kinds of distortion - and probably other things no one has figured out yet.
Distortion is unexpectedly complicated on its own. A while back I looked into models that use a Volterra series, and the math soon got very scary.
Doing it properly could potentially be a machine learning problem. I seriously doubt it's possible to reduce good distortion to a simple one-line equation - even a very long one with lots of coeffs.