Christopher Marlowe was born in the same year as William Shakespeare and they grew in popularity together. William Shakespeare was said to be greatly influenced by Christopher Marlowe, however. This implies that William Shakespeare got his start after Christopher Marlowe. Christopher Marlowe's short life was a mystery to many and his died of a stabbing before he probably would have produced the greatest of his works.
Whether or not Marlowe was, or could have been, greater than Shakespeare we will never know. Shakespeare seemed to be a fan of Marlowe, which is high praise coming from one of the greatest writers of all time.