Peter is like Cornelius and is not like Cornelius. Elijah is like us and is not like us.
Peter is different from Cornelius, in what he knows, in who he knows. He knows Jesus and knows his grace. He was a candidate of heaven while Cornelius was not. They may be similar in their physical attributes being men, but they were different in their spirits, in the core of their being. They are different in the relationship with God, not much as in religious practice. Cornelius gave alms, prayed and fasted but he was as lost as lost can be and needed Peter to preach to him the word of God (Acts 10).
What about Elijah? He was different in two ways: his passion for prayer and righteous stance. He stood for God in the most in auspicious times. He was attached to the cause of God both privately and publicly. He was so given over to him and cooperated with God to bring change.