Max Quad said:

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Best songwriter? Lennon, MccCartney, Harrison or Starr?

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Early Beatles. . . the team of Lennon and McCartney.

After 1968 . . . George Harrison

McCartney. I just don't care for most of Lennon's post Beatles work. I blame Yoko Ono - she has absolutely zero talent in anything relating to art or music

McCartney was a stronger musician than John. He played multiple instruments and taught John how to play proper guitar chords. (When John and Paul first met, John was playing banjo chords - i.e., only five strings - on his guitar because his mother had known how to play banjo and taught him those chords.) Paul initially played bass in The Beatles because the others didn't know how (and George was probably a better lead guitarist). And he could get on the piano whenever the power went out and they needed to play an acoustic set.

Because of his stronger musical skill, Paul was a more diverse songwriter than John or George.You see it most clearly on the white album; Paul's contributions seem to be a genre challenge. Can I write a country sounding song? Here's "Rocky Raccoon." Can I write a rocker? Here's "Helter Skelter." Can I write a parody/pastiche of the Beach Boys? Here's "Back in the USSR." Can I write a 1920's dance hall number? Here's "Martha My Dear."

Lennon had less range in his composition, but he also was more inclined to push into weird and experimental areas. Think "Tomorrow Never Knows," "Strawberry Fields Forever," "I Am the Walrus," and so on, not to mention "Revolution No. 9," which I always skipped. John also had a more acerbic wit (though George showed some of that in later years, such as in "Piggies"), and that made his songs fun to listen to.

George grew tremendously as a songwriter over the short life of the Beatles, with "Something" and "Here Comes the Sun" some of the best songs the Beatles did. He also learned to play sitar, which allowed the group to go into weird Indian-influenced areas, especially on "Within You, Without You." George also brought us "While My Guitar Gently Weeps," and his three album set All Things Must Pass after the break-up shows what he had been doing while John and Paul (and maybe George Martin?) were ignoring his stuff in the later Beatles years.

Ringo wasn't much of a writer, though "Don't Pass Me By" was a nice contribution.

My vote goes to Paul because of his greater diversity, but in the end a person's answer to this question is a matter of taste, like a favorite ice cream flavor or a favorite type of beer or soda. However, all of them were better when they were around each other, pushing each other to improve their songs and helping around the edges. That's why the early Lennon/McCartney stuff was so good, and "A Day in the Life" is IMO the best song that John and Paul really wrote together.