There's some interesting stuff out there on the subject. Beatles biographers seem to agree that McCartney was rather conservative, Edwardian, and establishment, making no attempts to hide his love for British Music Hall tradition. But he couldn't carry off something like "When I'm 64" without a dose of cheeky irony. And certainly songs like "Helter Skelter," tape loop projects (like the ones he brought to George Martin for Lennon's "Tomorrow Never Knows"), and concepts like Sgt. Pepper and the quasi-Kesey Magical Mystery Tour (despite the absolute failure of the film to be interesting) showed that he was no reactionary.
On the other hand, Lennon's reputation was pure rebel, no doubt a lot of it an affected James Dean pose. But Lennon's own body of work shows its own strong tilt toward sentimentality. "Good Night" (from the White Album) sounds like it could have been generated by the Disney machine, characterized as it is by swelling strings and mawkish melody. One must admit that Lennon's legendary "Imagine" is only a small, unironic step up from there. Lennon apparently thought, at first, that McCartney's sonic experimentation was no more than a lark, but he soon caught the progressive side of it. But if McCartney balances his streak of tradition with irony and experimentation, Lennon came to balance his with flat-out iconoclasm ("Revolution #9," "Two Virgins," etc.). Both had great faults. McCartney's more subtle, winking style could sound like uncritical, reactionary art. Lennon's in-your-face moralizing and pontificating often made his own art sound humorless and fatuously self-righteous. The old saw is that they balance one another in the group, but became self-indulgent on their own. Perhaps.
Maybe they just ran out of good ideas. It's hard to imagine the John Lennon who wrote songs like "Norwegian Wood" or "And Your Bird Can Sing" being proud of the crap he put out in the 70s -- although, as I've argued, if you strip away the Yoko stuff, Double Fantasy sounds for all the world like the work of a mature artist, unashamed of his own sentimentality and tired of poseur iconoclasm. Likewise, McCartney must have some reservations about the section of his solo catalog that might have been politely called "Adult Contemporary." To McCartney's credit, when he chooses producers and collaborators who aren't sycophants, the results can still be excellent. (See, for example, the streak of songwriting he did with Elvis Costello in the 80s and 90s, including tunes like "Veronica," "Shallow Grave," "You Want Her Too," and the haunting "So Like Candy.")
But the Beatles stuff still works well; forty years later, it still sounds fresh in a way that neither Wings nor the Plastic Ono Band do. There was something original and quite daring to the Beatles, despite the long history (blues) and pedigree (MusicHall/Pop) of their influences.