back in the day my amps were usually miked; if I could actually hear the stage monitors, when present, it was difficult to tell what my guitar sounded like with all the surrounded noise; this was more challenging if I was singing too.
I'd usually stand where I could hear my amp and the rest of the band in as balanced way possible. Having to be at a mic stand limited what I could hear, and at the mercy of the monitor mix.
when I first started getting into digital modelers, the biggest difference was what I heard in the room vs. the fully processed digital signal into FRFR. That was a common complaint and why some didn't use modeling for years maybe to this day?
When I'm just playing guitar at home, I'll use my tube amps. If I was recording, I would use my plugins; if I was playing live, I would my digital modeling rigs or a small combo tube amp.