Hah, I feel they all have the capability to be stubborn! :'D
Gonna focus on actual serious arguments.

And well, Reigen taking weeks of going throught it before finally apologizing for smth that really needed apologizing is a whole big plot point.
I think post seperation-arc he has learned from it & it isn't as extreme, but I think he will still need his time. I also think that Mob is very patient and will treat him more distantly throughout it, but never be mean or unforgiving.
I think by the end of canon Mob has become pretty good at recognizing when an apology is due - both from others & himself. Depending on what an argument was about, I can see Mob either apologizing right away, or being kinda mopey about the realization that he was in the wrong and needs to apologize & thus procrastinating it somewhat until he manages to get over himself.
Just the same, I don't see Reigen being very resentful about arguments. He certainly can be incredibly petty, but I see that happening more when the argument was about smth that isn't so serious, or when he himself is in the wrong. I think when Mob genuinely hurt or insulted him etc. that isn't the case.
tl;dr - the one in the wrong will apologize first, but it might take a while.
If they have an argument where they're both kinda right kinda wrong, I think Mob is more likely to make the first step, but he will want Reigen to see his side too. Most cases, it works out.

SasoDei............ Good lord.
Deidara apologizes earlier, because Sasori barely ever apologizes at all.
He does it with a roll of his eyes he doesn't even try to hide & it has a fair chance of making things worse. Argument is in the past, he lives in the moment - they had plans today, didn't they? He's very forgiving, but he rather just drop it all than talk about it or apologize sincerely.
Well, he's forgiving with most topics. If someone insults something that is important to his very core, he is so incredibly vindictive. Even if it was never meant as an insult.
I think they are very prone to miscommunication & one of my favorite situations is actually Deidara feeling deeply insulted by Sasori and Sasori being real with him. I love when it goes: Sasori says something that cuts deep, even though he never tried to -> Deidara is consumed by unreasonable anger near the point of desperation -> Sasori literally or figuratively grabs Deidara by the collar to lecture him in one way or another. "Your fragile self-woth is not my responsibility." "If you feel insulted by that, improve." or maybe even a generous "If you can't tell this was far from an insult, you don't know me as well as you think you do."
That's Sasori's version of an apology - graciously telling Deidara that he is in the wrong.
Deidara would still be angry first but calm gradually down & come to accept it, if it was a misunderstanding - because he prefers not actually being insulted or ridiculed for the things most important to him. And because I like my illusions of Sasori being the person to actually support him in his own messed up ways, that Deidara comes around to understand & even appreciate.
Anyway, if Sasori is in the wrong, well, they'll both know & that suffices. They will know the other knows, too. Topic dropped, they move on.
(All of this is considering canon where they're simply both far gone. I think in AUs they would still be pretty unhealthy in most cases, but there's potential for somewhat improved communication.)