Not even really sure what your title/post means ...
Do you mean an overdriven
sound, like an old tube amp, or a clean amp driving the speakers to the point of reaching their excursion limit?
I've heard a 100 watt Marshall Super Bass Plexi driven hard into a good 600 watt rated cab sound great
, and a GK 1001RB set clean bottom drivers in a cab "rated" to match that amps output and that sound was well nasty
... two very different things.
... Can we NOT do the whole "underpower" thing again ... and just say we did.