I have to support the reputation you have heard of for the Aspen Group. In Colorado, it is at the top of choices with four excellent ski areas to ski on a common pass, good at all four on the same day. Those areas are Aspen, Aspen Highlands, Buttermilk, and Snowmass.
Aspen holds a niche as a gathering place for the rich. The View from the top of Aspen Mountain out into the Maroon Belles wilderness is unrivaled on easily accessible lift served terrain in Colorado.
Aspen Highlands caters to the more adventurous skier. It should definitely be included in any list of adventure sites on the continent; like Jackson Hole, Taos, Kicking Horse, Snowbird, etc.. The Highlands bowl area is definitely not 'run of the mill' inbounds terrain.
Buttermilk caters to lower level skiers and boarders. It is pretty mellow with a few surprises mixed in.
Snowmass is a real special place, serving up what might be the best cruiser terrain in the continental US. It also has the greatest continuous vertical in the continental US and some surprisingly challenging features mixed in.
All in all the Aspen group serves up over 5,000 acres of terrain for all levels of skier, and feels confident enough with it that there is little mention of numerous backcountry possibilities. You can't miss with a trip to Aspen, but as stated earlier, there are many other options to choose from as well.
P.S. - It is a great ski area, but not generally noted as being one of the 'deep powder havens' you inquired about.