The Best Sounding Systems can Play Loudly with Low Distortion

I would say the very best sounding systems can play softly and sound dynamic and fantastic. They can also play loudly. Mine can play at ungodly high levels  without distortion... although I leave the room when someone wants to play them that loud. 

Being fully satisfying at low levels is a much harder feat and is the mark of a truly great system. 

I agree that the very best systems are impressive at how softly they can play and still sound alive and vivid.  This is the case with gigantic horn systems.  This ability is far more important because most listeners listen at modest levels most of the time.

While horns have the ability to play at very high volume levels, there are some other great speakers that are very limited in loudness capability, such as the Quad 57 electrostatic—cannot do deep bass, limited volume level, yet sounds so right.

Don't forget proper room treatment! It doesn't matter how good the system. An untreated room is easy to overload rendering it unlistenable.