I really really hate having the Beatles vs. Stones argument. First of all, as a whole there really is no argument to be had. In terms of aggregate greatness, one need only point to Voodoo Lounge and its putridly bizarre single "Love is Strong" to end the discussion.* The Beatles win simply because they never whiffed... even at their worst (Yellow Submarine) they were better than everyone else.
The argument gets a little more complicated however when you look at specific individual efforts from the Stones. Exile on Main Street is one of those efforts. Eighteen tracks of pure unadulterated killer with absolutely no filler. While hanging out in the French Riviera, snorting Tony Montana-esque piles of coke and banging European supermodels the Stones essentially invented alt-country while simultaneously setting the bar for rock music so high that no one even sniffed it** until the Ramones came around years later. The Keith Richards riffs on tracks like "Tumbling Dice" and "All Down the Line"*** exceed all but George Harrison's absolute best work with the Beatles (see below description of Harrison's best riffs), not to mention the fact that Richards plays with much larger cajones than Harrison. You can hear rock's future in his work... in each Richards lick you hear from artists running the gamut from Slash to Jack White.
The only problem with crowning the Stones' asses here is that Revolver is SUCH a monolithic force in the pop music canon. Ignoring the music entirely, the album is an incredible TECHNOLOGICAL achievement due to the production work alone. I think the music can best be explained by the fact that I had considered writing the following sentence but quickly thought better of it: "People just didn't do songs like Eleanor Rigby in 1966." I decided against this however when I realized that I could put literally any of the album's 14 songs into that sentence and it would still be unassailable. Revolver is just so much MORE than anything else of its time. You could argue that between Taxman, Tomorrow Never Knows, and And Your Bird Can Sing the boys from Liverpool invent punk, indie rock****, and power pop.
So how does one decide? Conveniently enough, I'm teaching the Renaissance right now in my history classes and as I plotted out this post I was reminded of a particular chunk of the curriculum. One thing that they learn is the idea of a "Renaissance Man" as someone who has talents in many areas. This image of course comes to embody the Renaissance spirit and sets the stage for centuries of creative genius. That having been said, Exile on Main Street is perhaps the best album ever at the one thing that the Stones were trying to do but Revolver is everything all the time. The sound and lyrics are profound in a way that no matter who your favorite band is you can hear them somewhere on this album... the sound is almost democratic. Not being one to buck democratic principles, I'll give the nod in this contest to Revolver by the thinnest of margins.
Revolver will take on Rubber Soul in Round 2. Next up, Blonde on Blonde vs. Pet Sounds
*Oddly, I remember MTV having a MASSIVE, overhyped rollout for the equally strange video for this song which, for those of you who have blocked it from your memory, constituted the band as giants walking around New York performing the song^.
^Strange 90s phenomenon: The absurdly expensive music video featuring outlandish special effects that cost millions of dollars back in the day but now would only cost like 8 bucks and a four pack of Red Bull in the hands of an adolescent computer geek. Other videos of this nature: 1. Black or White, Michael Jackson 2. Notorious B.I.G - Hypnotize 3. Hammer - 2 Legit 2 Quit 4. Missy Eliot - The Rain. Really anything with either Sean Combs or Hype Williams name attached to it works here.
** Not a reference to the aforementioned piles of Coke
*** My personal favorite... somehow he makes his guitar sound like a purring lioness.... this just blows off the top of my head
**** Tomorrow Never Knows sounds more like an Animal Collective songs than lots of Animal Collective songs