1st: "GreenEdge" is a proprietary term used by Harman/JBL, its only relevant to the upgraded JBL audio system that comes with the ATP package. All it means is that they maximize efficiency for minimal power consumption, use "green" materials, etc, etc. It has nothing to do with "audio quality" per se. The ATP JBL option uses better speakers and an amp, and does indeed offer substantially better quality especially at higher volumes.
This press release from Harmon from the 2012 launch of Greenedge on the Prius gives a nice description: Harman - Harman GreenEdge audio systems deliver more with less for 2012 Toyota Prius Family