Amp terminology: Touch Sensitivity
It seems that most of guitarists equate touch-sensitivity, sag, compression, and the "forgiving" nature of an amp. The opposite would be a "stiff" or "unforgiving" amp.
Obviously there's a spectrum of these behaviors, and I think there's at least one other category: "saturated" or "mushy" (different connotations, depending upon whether you like that kind of thing or not...). This is the sustain-forever kind of behavior, a la Santana, where touching the strings in virtually any manner will produce the same volume, if not the same tonality.
My preference is to have an amp somewhere in that middle ground where the behavior of the amp (whether it plays clean or dirty; whether it shimmers, growls, barks or screams) really depends on how you attack the strings. That's what I mean when I say "touch sensitive". This behavior almost certainly depends upon hitting the amp's "sweet spot"; if you run an amp's volume below the sweet spot the sound may become "stiff", "unforgiving" or "sterile", while above the sweet spot it may become "inarticulate" or "mushy".
When I was playing Boogies, I spent a lot of time trying to find that sweet spot. I found that the clean channel was generally far too stiff and the lead channel far too compressed. The Dumble-inspired amps seem to do quite a bit better, but the ones I've played have been voiced with a strong upper-midrange character that fatigues my ears after a while.