I experienced this myself. Between 2008 and 2016 I went exclusively AxeFX II with an Atomic CLR. I was not gigging so this "rig" was great for home playing and recording. A buddy of mine that does gig regularly stopped by one day and checked it out.
His response was "What the F**&^&^&? How can you play through his thing.? C'mon let's go to my house.
So I followed him back to his house with one of my guitars and walked into his "rehearsal room" .
He had a 1979 JMP MKII master lead with a tube screamer plugged into a 1970 4X12 slant top. I plugged in and "woke up"
What Jabps said above nails it, 2D to 3D. the sound had so much more "girth" and roundness to it, than what I got through my CLR. I felt so much more "connected" to my guitar.
I went crazy for about an hour and at the end I said "Ok I see what you mean".
So after that day I tried several power amps through "real" cabs (solid state and tube), but still couldn't get what I got at his place. then in 2015 I started jamming with a band . I brought my Axe "rig" with me, the other guitarist was playing through a Bogner Shiva and a 2X12 cab.
He completely "squashed " me. That was the end of the Axe FX rig.
Now I use a Splawn SuperSport El-34 through several different cabs (depending on the gig) and a CaptorX for FOH that I loaded an IR I created that is a blend of an Ownhammer 4X12 recto cab and a redwirez 4X12 Greenback cab.
Now I get the "feel" of my real cab on stage and the FOH gets a very consistent sound that I know always sounds the same.
So long story short " to the OP "I get it"
I do miss it for recording and late night noodling though.