I assume you're talking tube amps, Robert. Transistor amps are for kids! (that oughta draw some flame!)
Like most everything, it all depends. First off it might help if we talk about what a master volume actually does.
Distortion in a tube amp comes from 2 separate areas - the preamp and the power amp. The power amp is the big tube section just before the output transformer. The preamp is in all those smaller tubes that amplify just the guitar signal voltage, put it through a tone control stack and then feed the output tubes.
Preamp distortion is thinner and "fizzy". In its extreme form we get shred metal. Power amp distortion comes from driving the output tubes hard enough to compress the sound and saturate the output transformer. It's more warm and thick. That's the classic rock sound. Jimi Hendrix or the Young brothers from AC/DC.
Master volumes work by putting an extra control after the preamp stages and before the output tubes.This lets you run the preamp stages super hot and then cut it down to a much lower level to feed the output stage. You are controlling the amount of preamp distortion.
If you think about it, at lower master volume settings you can't possibly get any power amp distortion! You've dialed back the amount of signal going in to the output stage and there's no way those output tubes will push hard enough to saturate anything.
There are a number of different master volume circuits and some work better than others at having more effect at lower settings. The effect is only on the preamp distortion, however. The usual problem is noticing the effect at low master volume settings. The concensus is that putting the control after the phase inverter, which is the very last tube before the big output tubes works the best.
Even this approach still won't give you any power amp distortion.
If you play only metal this might be ok. If you want a more classic tone you're outta luck with a master volume. The thing about tube amps is they sound best for that tone if you crank 'em up! You have to be pushing enough power to make the power amp distortion happen.
I've seen a lot of guys take their 100 watt JCM 800 into a small club, telling themselves they'll just keep it below "3". Of course, it sounds lame-ass! So they can't resist cranking it up notch after notch. Halfway through the 1st set they're already pissing off the club owner! They just took too big a hammer to the job.
No carpenter would have only one size or kind of hammer or saw. Experienced guitarists are the same. I tell my customers to have a 20watt amp, a 50 watt amp and not to bother with a 100 watt amp 'cuz there just aren't any gigs big enough for most of us anymore. If you are at the level where you play big concerts you'll likely be miked anyway.
Please don't mention Pod pedals and the like. It's like an "edible oil product" Donald's shake or imitation bacon bits
I've built a number of 20 watt amps using the classic Marshall Plexi circuitry for guys that play mostly small clubs. They run 'em on "9" into a 2-12" or even 2-10" cab with efficient Eminence or Celestion speakers. They then can play "Hell's Bells" full out and still get re-booked.
If you have a master volume amp and still want that classic sound just leave the master on "10" and crank up the input gain control as high as you can. Leaving the master on "10" effectively puts it out of the circuit and lets the power amp start to work. You'll hear what I'm talking about!
---Wild Bill