Anecdotally at shows I attend and play, the less professional of a presentation, the more likely there are amps on stage. The bands that are well rehearsed with a prepared “show” are almost all running Kempers/Helix/QC (in that order of visibility) and then the closer to “punk” you get the more likely it’s amps. It’s not specific to an age range or genre. Anecdotally, of course.
Might be anecdotally, but I can share the same observations. There's varying degrees of modeling "percentage", though. Some folks are going all in, others (like me right now, at least for the time being) are using hybrid rigs, some are running into IEM systems, others are still using traditional cabs, etc.
On a possibly somewhat interesting sidenote: I see very little people doing it like me, as in using a modeler and a dedicated (read: just for their guitars) fullrange monitor. Most people are either running into an IEM setup, use the provided (or band) monitoring or run into some kinda power amp and a guitar cab.
I'm actually wondering about that a bit, because I found my personal wedge to be a pretty perfect happy medium. Allows me to use all the goodies of modeling (running my acoustic guitars through it as well, having independent monitoring level and EQing) while still offering some physical separation from the rest of the monitored signals (which I find to be incredibly useful) - and all that without having to use IEMs, which I only like for very loud gigs or tours with more than, say, 3-4 shows in a row (so I avoid them whenever the situation doesn't dictate them, such as on "clicked" shows).
Anyhow, modeling is creeping into pretty much all live areas and there's some kinda gigs which you wouldn't survive anymore without a modeling setup of some sorts (or at least a silent DI setup), such as pretty much all musical theatre shows and a whole lot of functional gigs. Regarding the latter, by now you even are expected to go for IEM, which I pretty much hate. Just last weekend I subbed for someone, brought my monitor as usual, drummer had an acoustic set, so I thought everything would be fine. Until I noticed the bass player had no amp with him. Yuck. So I had to go with IEM, too - which I actually hate on subbing gigs as there's no communication possible.