But, in my opinion to be one of the best rock bands you would have to be a great live band. The Stones were. They had arguably the greatest front man of all time and could hold an audience captive. Plus they put out a TON of music.
As an ardent Beatles fan I whole-heartedly endorse this comment. I love the Stones and I think the Stones had some pretty kick ass pop songs and the Beatles had some great rock songs but your assessment is a good one.