i agree with most here that technically JL wasn't the greatest, but The Beatles sound came from ideas, and that he had a lot of. He might not be able to translate some of his ideas to a marketable product unlike Paul who always seemed to know exactly what he wanted and how to make it sound that way, he still had lots going on upstairs and sometimes succeeded and sometimes failed.
The way that I look at what i call the "after break-up dialogue" between John and Paul, is just that. "How do you sleep?" was john expressing himself the only way he knew how. Do i think he was laid to rest feeling that way? absolutely not. I have said uncharitable things about people just because I was feeling hurt at the moment, too. Do i still feel that way years later? no. i just have the benenfit of not having my feelings etched into a whole bunch of records for everybody to hear about for the rest of my life...Thank God!!
I think john was searching as we all do and I have respect for him as a musician and an artist and someone who was really trying and succeeding occasionally.
edit: and anyway, years later john was to say "How do you sleep?" was more about himself than Paul anyway:
"Despite the overtness of the attack, Lennon later claimed that the song was more about himself than McCartney, and certainly one or two lines, notably "jump when your momma tells you anything", sound as though they are directed more at Lennon's relationship with Yoko Ono than Paul's with Linda. And the song begins with the puzzling statement "So Sgt. Pepper took you by surprise", a sentiment which applies more to John than Paul, the latter having been the principal driving force behind creating the album."