Mick: “To English people he was an enormous inspiration. Therein lies the difference because he was a songwriter, which Elvis wasn’t. And he wrote very simple songs, sort of lesson one in songwriting. Great songs, which had simple changes and nice melodies and changes of tempo and all that. You could learn from Buddy Holly how to write songs, the way he put them together. He was a beautiful writer.”
Keith: “Mick had been singing with some rock and roll bands, doing Buddy Holly… He was in England as solid as Elvis. Everything that came out was a record smash No. 1. By about ’58, it was either Elvis or him. It was split into two camps. The Elvis fans were the heavy leather boys and the Holly ones all somehow looked like Buddy Holly.”

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From Biography.com:
Buddy Holly was an American singer/songwriter who produced some of the most distinctive and influential work in rock music. Already well versed in several music styles, he was a seasoned performer by age 16. With hits such as “Peggy Sue” and “That’ll Be the Day,” Holly was a rising star when a tragic plane crash struck him down in 1959 at age 22.

After high school, Holly formed a band and played country and western songs regularly on a Lubbock radio station. He frequently opened for more prominent national acts that toured through town. Bandmate Sonny Curtis viewed Holly’s opening for Elvis Presley in 1955 as a crucial turning point for the singer. “When Elvis came along,” Curtis recalls, “Buddy fell in love with Elvis and we began to change. The next day we became Elvis clones.” Although the bespectacled, bow-tied youth lacked Elvis’s incendiary sex appeal, Holly’s conversion from country to rock ‘n’ roll did not go unnoticed. A record company talent scout soon caught his act at a skating rink and signed him to a contract.