Well, it's not exactly an equivalent. Deciding on when it works and when not is often hard for us.
I'd say it like that: "Jesteś człowiekiem!" either is a super Captain-Obvious thing to say, or it sounds like from science-fiction/fantasy. And while Spock or Elrond definitely are persons, they are not human.
"You are a person" definitely works in English here! "You are a human" is an odd thing to say in any context but a science fiction story. "You are a person" could be used in other contexts. Eg "you are a person so you deserve respect".
(Nice to see you admitting Spock is a person, though )