We do it both ways AT THE SAME TIME! The best of both worlds!
Believe me - my guitar player is all about setting the amp where he likes it - and letting his fingers make the sounds and dynamics flow (he loves the guitar's volume knob, too! - but mostly in the fingers). I wouldn't be his drummer for the last 20 years if he didn't have that kind of expressionism in his fingers

. I also loathe people that rely on the gear to sound like "them". My guitar player sounds like himself on any rig!
We use a
straight analog connection from Guitar > DI "Thru" > a small Peavey MAX Preamp for some added gain on the Strat Single Coils (clean tube gain and some pre-EQ shaping) > a Marshall Master Lead Combo. That's an older 80's Marshall 12" 30Watt solid state combo that gets LOUD for its size and power (has a Celestion 12" G75 IIRC). This path is FULLY ANALOG and COMPLETELY DRY and the combo is miked with a 57 and an e609 into a Demeter VTMP2a. There's your "Real Amp" right there

We supplement with the Amplitube / Marshal 9005 (now a Peavey CS800x until the 9005 arrives) / 4x12" 1960B which is also mic'd with a 57 and a HM1. This is the "fun/wet" part of the rig - but generally just has a Hendrix Rotovibe type thing and a few different preamp models - nothing too fancy. The 1x12" Combo and the 4x12" are actually about the same volume at practice.
We also record the clean DI feed to a seperate track for endless options in the mix (re-amping, another Amplitube instance, a clean track to add clarity, whatever we need).
This works well because the guitar player also practices through Amplitube at home - so he can get a patch setup and bring it to practice and load it right up (he also runs a 4x12" at home, but a cheap Fender cabinet on my Sony TA-N55ES power amp).
I can't say I've seen to many rigs like this one. Many are FAR MORE complex - but not really any more versatile IMNSHO
