Should the Avengers be totally unsupervised or obey a government agency?(We'll assume here that the Marvel-UN is composed of democracies and enlightened monarchies such as Wakanda, not the tyrants and kleptocrats of ours)
Tony Stark/Ironman, reeling with PTSD and guilty over collateral casualties, decides to give up on privatizing world peace and sign up for adult supervision. Steve Rogers/Captain America isn't willing to subordinate his conscience to anyone else's. As superheroes do, they settle this by punching each other.
Tony's issues are clear (and were outlined very well in DrNerdlove's "Tony Stark Needs a Hug"). Captain America is the interesting one for me. The magic potion given to him in WWII boosted his attributes. In D&D terms he has maxed out Strength, Dexterity, and Constitution (for brawling) and Charisma (for leadership and selling war bonds). He didn't get max Intelligence--he doesn't challenge Stark and Banner on facts and he accepts Fury and Romanoff's plans, so he's fine with deferring to smarter people. So the question for this movie is: What did the potion do to his Wisdom score?
He's certainly acting like he has max Wisdom. He has no doubts, he's always making the right choice, he doesn't need to ask any advice about the goal should be. So Cap won't subordinate his conscience to any government, no matter how much popular support it has. If you're on the side of the Truth, you stand still and tell the whole world, "No, you move."
Inspiring. Of course, that depends on him actually being right, and his obsession with protecting a reprogrammable assassin makes me doubt what his actual Wisdom score is. But I won't get into the spoilers.
When it comes to choosing Team Cap vs. Team Ironman I don't have to put much thought into it. I wrestled with that decision some 26 years ago. The Air Force assigned me to my chosen career field and let me go play with satellites. But one of the other duties of that specialty was launching ICBMs. So I had to face the question: Would I launch a nuke if I was ordered to?
I decided yes, I would. And conversely I wouldn't launch a nuke without orders, regardless of how much I thought the target deserved it. Because my Wisdom score isn't maxed. I make mistakes. And history has plenty of examples of why letting armies pick their orders is a bad idea.