Debate is the art of persuasion. It includes emotional appeals to others and framing an issue. Additionally, one must consider his or her opponent and how to respond to that person. The winner of a debate makes an artful and rational argument with ease. Someone who was unprepared and had not studied the art of debate would not do as well as someone who had studied it.
Are you debating something that depends on statistical fact & observed facts? Then it's a discussion. Are you debating something that depends on belief or opinion? Then unless it's religion versus athiesm, because most of those arguments are stats not opinion, it's technically art. Art can't really be defined, but the closest we can come is saying creative power used to make something. Trying to determine various philosophical concepts by discussing them uses creativity in your brain to keep you thinking of ways to argue. Sure, movies & paintings are way more so art than debate, but is' somewhat art. Again, it depends on the debate itself though.
The principle of dialectic debate is one which sees thesis meet anti-thesis, Producing a more accurate theory which is then offered again as a thesis. Debate only becomes an art when you tolerate the use of logical fallacy. If fallacies are prohibited then debate really becomes a process of reasoning.