"Which one is correct?"
Be careful of "to be" as a verb; many times it doesn't follow the rules for other verbs. Also, "what" is a very general question. You've given two options, so "which one" is what you need to ask.
"Tell me about yourself" is correct. "Tell" is imperative (as in "I want you to tell me..."), so the other person will speak, and the topic will be the speaker. The performer and receiver of the action are both the same person, so we use a reflexive "-self".
She told me about herself.
He'll tell us about himself.
They told me about you. (Subject and object are different here.)