Never talk about yourself; steer the interview to being about a problem they are solving with work and help them run through how you would solve the problem as if it's a meeting and you are working with them. Rarely fails.
I'd say it's not either or. Do both. Give a short summary of who you are with related projects you worked on. Explain shortly how these experiences made you an authority on their problem. Then explain how you would handle that problem of theirs.