Here's a rule-of-thumb that I go by: Whoever takes the other side into account best is the winner. For example:
Side 1: Language x sucks because of y!
Side 2: While it's true that x potentially sucks because of y, y is easily mitigated by z, and y still offers benefits a, b, & c that most other languages don't.
Even if you have only a shallow understanding of the argument, it's easy to see that in most real-world arguments Side 2 should win.
It's related to who gets angriest because people usually get angry because they have run out of other options.
What if the other person is just being an idiot? What if you think he's not capable of understanding? What if he's a child? What if you think he's trolling? Is better argument still the way to go?
I am a parent, so I can answer your question with respect to children: raising your voice does not do anything except escalate the discussion into an emotional melt-down.
With respect to people you deem to be idiots and trolls, we have known the answer for a very long time. One of the more amusing bits of advice about the matter came from Mark twain:
"Never argue with a fool, onlookers may not be able to tell the difference."
I agree that yelling at children doesn't help. But I'm wondering if you would debate with a child, or try to persuade him with good ideas, or would use some other sort of approach that isn't yelling or persuading?
It's not useful as the only predictor, because people's emotional involvement in ideas can vary, but I find it to be useful meta-information.