Dialogue involves a real concern for the other person and seeks to not alienate or offend. Debate involves a countering of the other position without focusing on feelings or relationship and often belittles or deprecates the other person. Dialogue assumes that many people have pieces of the answer and that together they can put them into a workable solution. Debate assumes that there is a right answer and that someone has it. Dialogue remains open-ended.
Debate implies a conclusion.