It should be understood that each amp manufacturer, each model, and each technology, have, inherently, very different tonal responses to controls in the (very different...) pre-amps, so there is very little commonality between them. The settings, and range of result, cannot be equated from one to another. The reasons are as varied as the amps themselves : solid-state does not behave as valve stuff, and EL84 valves do not behave like KT88's etc. The effect of 'gain', 'master volume', tone controls differ; some tone circuits are 'flat' with the control at centre, some with the control max anti-clockwise, some (many..!) are never really 'flat', whatever the setting..!
All of these factors make every combination of amp-cab useful for its own range, but maybe not so good at another. What sounds good at home may well not have what it takes on stage; even less so on a stadium stage. It works both ways, too; the only way to get a Marshall stack to belt out 'that' sound is to crank it, which makes it a poor candidate for bedroom practice in a town centre high-rise block of flats.
In sum, it's 'horses for courses'. One amp for home, another for rehearsals, maybe another for gigs... This is one (of many...) reasons for the advent of Fx pedals in the first place : the ability to 'dial in' the required tone at any volume.
It doesn't surprise me at all that the Classic 20 doesn't 'cut it' on stage. Despite having the same power valves (EL84...) as the Vox AC30, the circuits and cab are not at all the same, and the tonal response are chalk and cheese. You can never get a really clean sound from a Classic 20, at pretty much any volume; that's not how the circuit has been designed. They don't do 'loud'; certainly not the 'loud' that an AC 30 does.
What are your options..? Find an amp which has the tonal variance that you need, in all the situations, you'll be playing, or have a different amp (and settings...) for each usage, or start building a pedal-board around an amp which ticks most of your boxes. It's not really a case of 'SS' v 'Valve' v 'Modelling'. It's just that all rigs have their upside and downside. Such is Life. Hope this helps.