It should go without saying that some of these other answers have very valuable advice that is definitely worth reading.
When people "debate" it is rarely calm and cool headed. It rarely stays on topic and quite often comes from the fact that the basic assumptions which each has hitherto assumed the other also held are different.
This is a great time to expose any character flaws (which I assume you have thought about because you strike me as a sensible writer) and have a good opportunity not just to exposition the situation to the readers but also show the characters dealing with their conflict.
When I want to turn up the heat in a character debate I try to stay laser focused on what exactly the bone of contention is but allow the characters to throw in unrelated things that the reader might not be fully aware of (or was nto present for) but the characters know as they have a shared history before the story started.
The core disagreement should be something that can be expressed in not many words and doing so helps to clarify the positions of the two characters more clearly in my mind. What can really make an argument bitter and drawn out is when the words people are using clearly mean something different to each of them.
I have seen two very liberal Christians spend hours debating a single issue that from the outside it might seem that they are both agreeing rather aggressively with each other on. This is because they have assigned vastly different meanings tot he same words. As the debate gets heated there is the odd slip to bringing in unrelated barbs. This is where the art of subtext is really important.
It also allows the debate to go meta (which happens) where the characters have to "side bar" in order to thrash out what some word or phase means.
Further it can really help to give the emotional reaction too. Remembering that it is not so much the thesis of what they are saying that brings character to the front but their emotional reaction to each other.
"No, that's not right at all" said Bob as he struggled to not let his
frustration with John boil over into actual shouting. Why can he not
see how wrong he is on this?
"I don't think you are hearing what I am saying," said John feeling
that Bob was not listening to him properly. "This is not the old 'out
in the military' debate, this is about saving lives."
"How the hot hell do you mean to save lives by ending them?" Snapped
Bob more angrily than he intended.
In the above example, which I invented just now (feel free to use and abuse as you wish), I have tried to say nothing at all about the actual debate and yet the two speakers are getting really irate over the issue all the same. Not all debates are filled with people giving good articulation to point and counter point. People are irrational and can sometimes simply communicate very badly. Make use of this as needed.
If this were part of some actual narrative we would have learned that these guys have had debates like this before and do not agree. It says a lot about John and Bob without actually adding anything new to the debate itself which, sadly, is how most people carry on.
TL;DR: let the character's passion show in their dialogue.