I think one of many things which set them apart from and above everyone else was their intangible ability to be "All things to all men". Even in their supposedly simplistic early days they were pathfinders, breaking new ground with deceptively clever chord progressions, introspective lyrics etc. In the later, studio-bound experimental years they somehow still retained that cross-generational, radio-friendly mass appeal.
I cannot think of anyone else who could combine all of this re-invention and sustain it so authentically and consistently for so long on so many levels. They wrapped it all up in quicksilver humour and delightful sponteneity which left their peers and successors lumbering. Of course the teenagers fell for them, but Grandmothers and infants loved them as well and so did concert pianists and cynical music critics. God knows how, but aside from those poor unfortunates who've never been able to "get it", they never lost traction with either end of the spectrum whilst wooing and wowing the other. I really don't think anyone else could do this - and keep on doing this - like they could.
It's as if someone with broad but relatively shallow popularity like, say, Take That or The Osmonds had the gravitas and cool credibility of, for example, Pink Floyd... or to flip that around, imagine someone with the rock credentials of Cream or Jethro Tull simultaneously sustaining the commercial adoration akin to that of Abba or The Backstreet Boys. A clumsy analogy, I know - but if you could then blend all the positive elements out of those combinations, multiply it a hundredfold and mix in a considerable splash of magic, in my opinion you'd still only be approaching the once in a millenium freak brilliance of John, Paul, George and Ringo.