The 61-year-old rocker recalls how the pair jousted creatively in a flurry of ongoing musical one-upmanship, but he admits Lennon always managed to top him.
He says, "I remember reading that when John heard COMING UP he said, 'Oh bastard McCartney. I've got to write again!'
"It reminded him of the standards we both could reach. It's interesting that it was a little song like that, not particularly earth-shattering.
"It would happen to me too. I would hear something and go, 'Oh, here we go again.'
"It was like a see-saw. He'd write NOWHERE MAN, so I'd have to write PAPERBACK WRITER.