Loomis,
The distinction between our views may be real or it may be more semantic.
I use "songcraft" to mean sophistication in a few areas - but, in the end, it's first and foremost (tho not exclusively) a harmonic distinction to me. What I call "true" rock n roll has about zero harmonic sophistication. The chords are rarely inventive and may even add only a single note to the root. There are few to no vocal harmonies. The greatest examples (see "Johnny B Goode) are so simple - backbeat/riff/lead guitar/maybe a throwaway vocal - that they're barely even songs. The lead playing is compelling and doesn't even respect the most basic of rules, moving seamlessly from major key to minor and back. The real joy of the music is in the LEAD guitar backed by the rhythm (let's call it "guit- art").
To me, the absence of harmonic interest is - in one respect - a huge plus. It forces the artist to work with a limited toolbox and, at its best - finds treasure in absolute simplicity. (That's also what I'm driving at when I cite a lack of songcraft.) It also recalls the music of other cultures where tempered scales aren't common and harmony doesn't really work.
One of the reasons that I really love that kind of "true" rock n roll is that - like so much controversial 20th century art - it rejects the idea that the historical bedrock values of the art that preceded it (e.g. harmonic sophistication in music) are sacrosanct. Chuck Berry (and Andy Warhol, for that matter) provide a challenge to the status quo that raises their work to the level of serious art (for me), even if many folks here on the 'Gon would disagree with me. Lots of people reacted violently to these artists because they did present a challenge to existing cultural standards. (The book Pirate Radio points out that British cultural authorities were willing to literally kill to keep rock n roll out of England.) Because - That way lies anarchy!
The Beatles (by their own admission following closely in the footsteps of Brian Wilson) added tremendous harmonic sophistication to the basic rock n roll formula. They became the standard bearers of the "Disciples of Brian", nearly all of whom also became less "guitar centric". (The lead break on Good Vibrations, for example, is played on electro-theremin.)
While there's tons of interesting guitar work in The Beatles' catalog, IMO there's very little in the way of compelling guitar leads. Paul McCartney goes up the neck in tenths on Blackbird - clever guitar playing, no doubt, but IMO closer in spirit to Bach than to Berry. I'd argue that they favored guitar-craft over guitar-art. On the one hand, they provided a new way forward - out of the Berry box, if you will. On the other hand, you could argue that they undermined the whole idea of rock n roll in doing so.
The Stones (and most "hard rock" bands) took another route out of the box. Unlike The Beatles or The Beach Boys, they rarely let harmonic ideas become the central point of their art. Chords stay simple, instrumentation stays simple, tonal color stays simple. Mostly, they find variety within the guitar playing. Of course, making a pure, hard distinction would be an overstatement. In reality, it's more of a sliding scale. The Stones offered some songcraft and The Beatles offered some guit-art. But to me, the difference in emphasis is what really separates the two great bands.
One way to summarize it: The Stones always tried to stay closer to historically African American roots of the form, while The Beatles moved to a sound that was more traditionally Western.
My point about The Stones being well understood and also under appreciated was merely that most folks prefer songcraft to guit-art.
I'm not even really calling a favorite here. I write a half dozen songs a year and The Beatles (along with Stephen Sonheim) are BY FAR my biggest influence. However, when it comes to listening, I'll take The Stones 9 times out of 10. As noted, more often, I'll take Lindsey Buckingham because he provides a satisfying measure of each: songcraft, guitarcraft and guit-art. He's clearly a Disciple of Brian, but he's also a wildman with a guitar who preserves the essential anarchical elements of rock n roll in much of his music.
To be clear, this read on the issue is purely my own. I don't expect anyone to particularly embrace it. But it is definitely the way I make sense of rock n roll and the question of The Beatles vs The Stones.