The relationship is super predictable though? Its not like trying to predict weather patterns, or even a projectile's path in a moderately windy environment.
If you are running the modeler through something other than the same speaker cabinet you are running the amp through, then of course you're always going to fail - though Jay might come very very close given the very unique IRs that he has captured of some of his cabinets. And of course you need a power amp that is up to the task.
If you are playing the amp and the modeler at different volumes, of course its going to feel and sound different.
Assuming you are doing the above, and the amp you are using is one that is modeled in your modeler, you still have two hurdles left: (1). how close to the amp that was modeled is the amp you are playing, really? (2). On a non-master volume amp you've got a volume knob. On a model of that amp you have a master volume knob and a volume knob and then an output level from the amp block (and likely at least one more master output knob for the modeler) -- so gain staging the "modeled amp" the same way the amp itself is gain staged so that its accurately modeling what the amp is doing while also volume matching is...hard.
All of this is to say: if the exercise is to get a modeler to sound exactly like an amp you own and enjoy playing...that is a whole lot of work. You SHOULD be able to get really, really close...close enough for plenty of people not to notice a difference, even when playing. But...what's the point? "Hey, I'm playing a different thing at the same volume as this other thing that I already own and they sound the same!!!"
However, someone making super broad blanket statements that every digital model of every amp is inherently more compressed than the amp even if you can't hear it when that same person somehow thinks that a modeler should be run through an ""FRFR"" speaker in an attempt to sound like a guitar amp that is playing in the same room through a guitar cab is equally dumb. And not because digital fanboys are butt hurt, but because it leads people like merciful who has little to no experience playing through amps to start endless threads gnashing teeth over whether their at-home playing experience is somehow compromised by anything other than monitor, volume and skill limitations.