We forget that a 'dark side' doesn't necessarily mean evil. It can also mean the obverse side of a trait which can also be positive.
Tony's genius, for example, is that he's intuitive and can make large leaps forward to conclusions. Sometimes, that works for him -- take, for example, his being able to intuit where Loki will strike in the Avengers. However, the dark side of that talent strikes when he fails to think past that conclusion -- Ultron being a shining example there.
Cap stands for what he believes is right. He's an incredibly tenacious person; any lesser person faced with what he's been through would have been huddled in a corner gibbering, not going out and trying to protect people.
That said, the flip side of tenacious is stubbornness, and idealism without realism is incredibly dangerous. Also, while Cap is loyal to those he cares about, he is loyal first and foremost to what he believes is right and, as he's said in the comics, the American Dream -- i.e., the ideals of what America is supposed to stand for, or rather, what immigrants like his parents dreamed America was - freedom, opportunity, equality.
Which means that loyalty to people -- even those closest to him -- comes second after loyalty to principles and to what he perceives as his duty.
He crashes a plane to save millions rather than ditch the plane and go back for that life with Peggy, for example.
And no matter what we see in the trailer re: Bucky, he also would and could have killed Bucky if that was the only way he could have brought those helicarriers down. Granted, he tried his very best not to do so and it would have killed him to do it, but there's no doubt he WOULD have, if that was the one and only way he could have saved millions of people. Only AFTER the helicarriers are safely taken care of does he stop fighting and focus on trying to break Bucky's brainwashing. And this is the guy who would have (some would argue, did) die to save Steve on the train AND the guy he loves like a brother.
So it's small wonder he'll fight Tony if he must. Also, that view is not something Tony would understand. Tony's a man with few friends and once he's given his loyalty, it's to people first, principles flexible.
Also, Cap absolutely does not surrender and he's worse at compromising.
The problem with that is that it inevitably leads to Pyrrhic victories and endings like Thermopylae. Sometimes, no ideal is worth fighting to the last man. Sometimes, it's better to compromise, to have balance.
And Cap can't always do that. Although his goal is to protect people, his idealism and stubbornness means he can lose sight of that and put principles above people.
In the comic Civil War, in fact, that's exactly what happens -- Cap's winning, but realizes, far too late, that innocent people are getting hurt because he's done exactly that -- stuck by his principles without counting the cost to others. It's why he stands down, but by then, it's too late.
And putting principles above people can be fatally easy for him because he has nothing to lose, especially in the MCU. No home, no significant other, nothing BUT those principles.
IMO, that's why, to me, lawful good people (to use the old D&D term) can be far, far more terrifying than any form of evil. Good at any cost can be even more devastating than evil.