I think there are a lot of subtle things that contribute to it....most of them to do with how the volume in the room interacts with the guitar and the fact that guitar cabs are actually really terrible speakers, at least in terms of accurately playing what's fed into them.
The biggest things, to me, are how the guitar responds to the volume in the room (which Fractal can "fake" very well), some of the electrical interactions (damping factor, OT loading, pickup loading, etc., which fractal does the same or better than other modelers), and how you hear a loud cab in the room compared to however you listen to the modeler.
The first "big" eureka moment for me was when I spent some time setting up the amp output compression and played the fractal into a studio monitor that I put on the floor behind me. It wasn't perfect (because the studio monitor still interacts with the room very differently from a cab...it's directivity is made for fidelity as opposed to the guitar cab's directivity being more a matter of "whatever you get when you build a cab like they've always done"), but it was a lot closer than anything else I'd heard. And in many ways, it was flat-out better than every other way I'd try to play electric at reasonable volumes.
The output compressor, IMHO, fixes all the feel things once you tune it to the volume in the room.
The next big one was after I realized that everything I was experiencing was different from what anyone else ever experienced. Which actually came from buying my first acoustic guitar, years and years after I started playing electric. I'd played acoustics before but never owned one.
Every single acoustic I played, from $80 to $8,000, sounded substantially better when someone else was playing it. I thought that maybe I just sucked. The employees said I sounded fine, which I didn't trust because they were trying to make money (can't blame them). I did some stupid, low-quality iPhone recordings (in the store) of an employee playing a couple guitars and me playing the same guitars...and despite the crappy recordings, each sounded much more like what I was hearing when someone else played each one....not exactly the same, we were different players with different hands and different minds, and I didn't have my good IEMs with me, just the super bright wireless ones I used for podcasts. But, it was still closer.
I came to the conclusion that no acoustic was ever going to sound "right" to me when I was playing it because all acoustics sound better to me from in front of the guitar than above it. No one ever mics an acoustic guitar with a mic where the player's head is.
Which lead to two big ideas....
First, since I just have the acoustic to tick a box and don't feel inspired to focus on them anyway, what I hear doesn't matter that much as long as I can tell what I'm playing.
Second....as dumb as it sounds....the "right way" for me to be inspired to play my acoustic is to set up microphones and monitor what's coming out of the front of the guitar through IEMs.
And then I realized that the same thing happens with electrics. Whether it's going to FOH or a recording, what I'm experiencing when I play in front of an amp is fundamentally different from what everyone else experiences after the engineer puts a mic in one place, high-passes the crap out of it, and makes it sound good in the context of the rest of the song....or when anyone else stands not exactly where I am in the room. If I want to inspire other people with my music, I need to hear what they're hearing and have that inspire me....which a lot of people do a lot of different ways.
Now...guitar is just a hobby for me. I'm describing it in more general performance-y terms because it's easier, but that isn't my life. Really...I just want to be inspired and enjoy what I'm doing without blowing out my ears.
And as dumb as it sounds, after all this....the easiest way for me to do that doesn't involve a speaker. I make it sound good in IEMs that I really like, set up the output compression to work with a "silent stage", and route whatever I'm playing with through the fractal to minimize latency.
It doesn't bother anyone, I can play whenever I want, and it's easy to bypass an EQ block to get an inspiring sound by myself or turn it on so it fits with whatever/whoever I'm playing with, and I get an inspiring sound from the song. It makes casually playing with other musicians a lot harder....but it's worth jumping through the hoops. And, frankly...it happens a lot more often with the acoustic anyway because of who my friends are and how we play together. And I don't like my sound that much when we do it...but everyone else is fine with it, and I can play with them and be inspired by the experience.
So...yeah...a year or two of experimentation took me from "there's something missing" to "I only want to play on IEMs" and when I don't get to...then I really don't care that much about exactly what I'm hearing as long as I can hear well enough to play, and I can get inspiration from listening intently to everyone else at least as well as I can from listening to myself.
Sorry...big ramble. Basically, I think it's a non-issue.