To me, the Axe-Fx excels in the quality of its tones, and at being completely, infinitely tweakable.
For recording or playing gigs with your band, having decent soundcheck opportunities, it’s pretty hard to beat.
HOWEVER, if you’re in any kind of environment with new or unknown variables, like where you will need to improv or tweak/adapt your sounds to the musicians around you in real time, and you don’t have a computer running the editor in front of you, there is simply too much menu diving required for most people. I can completely understand some people just not getting along with the workflow. That said, I personally think the front panel is fantastic for what it is, and love Fractal’s overall approach to UI design, but given everything the Axe-Fx can do, there is no front panel interface I can think of that would give you anything approaching a WYSIWYG style, “1 controllable parameter = 1 physical knob/button/switch” traditional interface you get with real amps and pedals.
I love my Axe-Fx and will happily use it if I’m ever recording or playing pre-rehearsed shows. I’d even say that if I had to choose, I’d pick it over my tube amps and real pedals.
But for just having a rig to show up somewhere new with? I’m sticking with a traditional amp and pedalboard with straightforward effects. Even though they are more limited in the total scope of the sounds they can give you, their ability to let you immediately tweak any setting within that smaller scope is preferable and just easier to work with over modeling's infinite sounds that require preparation and menu-diving to achieve. And nobody, nobody, wants to sit around and wait on somebody to poke and prod at their gear to get it to work for them, killing any vibe that might have been building.
tl;dr:
Modeling, or at least Fractal's modeling, is preferable when you have time to tweak. However, traditional rigs are preferable when you need "tonal agility" in new or improv settings.