There's a lot of received crap out there about how Macca wrote rubbish and Lennon was some sort of genius. Yes, some of Macca's solo stuff was banal. But if the pro-Lennonites are claiming that Lennon never sunk to those levels, they're deluding themselves. He turned out his share of bland, album-filling pap, no question. But I love #9 Dream, Mind Games and Instant Karma.
As far as the Beatles are concerned, it's close but for me Macca edges it. I'd like to assume the person who said "Hey Jude is the only song worth a listen" was being provocative - even allowing for personal opinion, that's a tad extreme for anyone with any kind of liking for the Beatles. Penny Lane, For No One, Eleanor Rigby, You Never Give Me Your Money, Getting Better, We Can Work It Out... none of them worth a listen?
I also respect Macca's role more - by most accounts he seemed to become the main driving force and creative thinker in the latter half of their career, while Lennon became increasingly uninterested. Nothing wrong with that, it's just that I warm more to Macca for his working hard to keep things going.
To echo what someone else said, let's not forget Harrison's songwriting contributions - Taxman remains one of the best album openers ever, Something is one of the best love songs ever.