The same type of overexposure regarding Bach, Mozart, Beethoven, et.al. that have left no mystery for 200+ years?
No. There is plenty of "mystery" left in their stuff: different interpretations, transcriptions, instruments, and the music itself has so many layers to consider; from listening to the great melodies ("tunes"),to how themes are worked out, etc. As Tvad aluded to, a Bach piece can be played on an organ, by a brass quintet or a full orchestra. It's still Bach, but it's different and interesting. A Beatles cover by some other singer or band just ain't the Beatles.
But as to the qn. about the two bands; I never understood the fascination with the Rolling Stones. On some of their studio recordings instruments and vocals are painfully out of tune. Or is that part of the fascination? As somebody pointed out, the Beatles were the best song-writers since Schubert.
A fifty-one-year-old fogey,
Steve O.