These disputes' final goal is to demoralize opponent and make him flee the battlefield. Common method to determine winner is to see whose phrase is last.
Lots of tactics can be employed in this kind of dispute, and factual ones are useful only with smart audience. Generally demagogical tricks are the most useful.
These disputes, if held by clever people, often enlighten both opponents and it's hard to determine winner, because both participants usually adjust their points of view and end dispute in peace.
Using demagogy is usually frowned upon, but if audience is not too bright/experiened, dispute can be converted to emotinal one.
In short, use whatever can throw your opponent off balance. If you can find a weakness, exploit it. Common tactics include:
1. Pointing out opponent's low age and social failures.
2. Ridiculing opponent's accent, grammar mistakes, etc.
3. Considering opponent frustrated by ongoing dispute.
4. Showing off that you don't care about how the dispute ends, your happy mood (smileys help a lot).
First off, factual responses to emotional arguments don't work. Opponent can just ignore them, and you look like a fool trying to change his opinion. Instead, just ignore the insults and counter-attack with factual arguments (regarding dispute's object, not yourself).
Counter-attack with emotional arguments, taking them to new level. This counter-attack requires high skill, and leads to power-levelling, so eventually one of you will quit and the other will win.
If opponent uses factual tactics with small portion of emotinal, carefully examine his arguments and point out the emotional parts, then counter the factual ones.