Which record company turned down The Beatles, but signed up The Rolling Stones?

May ,1963
Rolling Stones sign with Decca Records. They are signed by the same A&R man who had turned down the Beatles the year before.

Decca Records is correct.

If all the A&R guy heard was the Beatle's demo of "The Shiek of Araby," he did the only thing he could do. I found it on Napster, and it is beyond description, even with the knowledge that it was made at a time when good rock was very rare.