In a debate you search for search for weaknesses in other people's ideas. In a dialogue you may consider new ideas and even change your mind completely. In a debate you do not admit you are considering new ideas and you must not change your mind, or you lose. Dialogue encourages you to evaluate yourself. Debate encourages you to criticize others.
Dialogue promotes open-mindedness, including an openness to being wrong.
Debate creates a close-minded attitude, a determination to be right. Dialogue encourages you to see all sides of an issue. Debate encourages you to see only two different sides of an issue. Dialogue invites keeping the topic open after the discussion formally ends. Debate, by creating a winner and a lose, discourages further discussion.