Tostado,
You raise a fair point in that Squeeze is essentially playing on the same musical field as did the Beatles - combining the rhythmic conventions of rock n roll with a richer harmonic approach. While The Beatles can fairly claim IMO a more sophisticated and innovative legacy on that front than can Squeeze, the question of songwriting preference isn't limited by that distinction. Chris Difford is simply a remarkable lyricist.
Both John and Paul produced some memorable lyrics and Lennon is remembered in some quarters as a poet. Personal preferences differ, but IMO neither Lennon nor McCartney can touch Chris Difford for narrative lyric writing. The bulk of popular opinion might take issue with that statement, but it's my personal judgement.
Even if you're willing to stipulate the above, it's still fair to ask whether that is enough to defend the notion that Difford/Tillbrook surpasses Lennon/Macca as songwriters. In the end, the answer to that question depends upon your priorities. For me, Squeeze is good enough on the tune smithing front to make any edge the Beatles have in that realm essentially irrelevant. Again, that's just my own personal priority at play.
At the end of the day, I simply never go back and listen to the Beatles anymore. They sort of ended up as neither fish nor fowl for me. Their achievement may indeed be impressive within the bounds of what they set out to do, but i guess that I find that it more clever than it is nourishing. These days I want nourishment.
I fully appreciate their craft, but - if I need a shot of harmonically rich popular music - I'll probably fire up some Stephen Sondheim. If I want rock n roll, I'll fire up some Rolling Stones or Chuck Berry. If I want something in between, I'm more likely to turn to Squeeze, Brian Wilson, Lindsey Buckingham etc. than I am to turn to The Beatles.
I'm not about to try to convince you (or anyone else) that one band or the other featured better songwriting. I can only tell you that I much prefer listening to Squeeze these days.
As a side note, George Harrison definitely had his moments (as I noted previously, the solo in Something is among my absolute favorites) but I personally wouldn't consider him a great rock guitarist based on his work with The Beatles. After he left, Harrison made a better case for himself IMO, but The Beatles catalog offers little guitar soloing that I find worth revisiting. There's plenty of compelling arrangement of music for guitar, but only a little lead that floats my boat.
It doesn't need to be said, but YMMV.