I think it should be known that as I was typing this up, I was originally going for Team Iron Man, but you can see that as I go along, I slowly start to have a mental tug-of-war with myself on the issue. That just goes to show how much this starts to tear me apart.
I'm basing this mainly off of the comic book, Marvel's Civil War by Millar, McNiven, Vines and Hollowell. In the book, as Congress is going over the Superhero Registration Act, Cap goes ballistic, beating the snot out of a ton of S.H.I.E.L.D. agents, and escaping via hijacked plane. Throughout the entire story, Cap acts irrationally, ranting on about how if they went through with it, "the government would be telling" them "who the bad guys are." For one thing, is that entirely a bad thing?
Shifting focus to the upcoming movie, you can tell that Rogers is going to do the same, only he has a better reason to do it: if the government has their way, it would basically mean the end of his childhood friend, Bucky. In fact, they would probably have him help with the manhunt himself. It also provides a better reason for him to be fighting his new friend, Tony Stark, AKA Iron Man. In the comics, he just does it out of stubbornness, and he doesn't even blink when denying Tony's outreached hand. However, it seems like in the movie, Steve will be slightly more reasonable than Tony, as Stark shows signs of feeling betrayed, especially in this dialogue:
CA: "Sorry, Tony. You know I wouldn't do this if I had any other choice. But he's my friend."
IM: "...So was I."
And also, we see in the trailer Stark holding Rhodey, AKA War Machine AKA Iron Patriot (he seems to appear as War Machine this time), heavily damaged, and quite possibly dead. The way the story's going so far, I would say that Captain America had something to do with it, no matter how indirect. This would very likely set Tony off more than ever before, and I'm also talking about the time he sent a terrorist his home address after Happy, Tony's former bodyguard, was a victim in one of the Extremis attacks in Iron Man 3. This would make it a battle for the best friends: one will be attempting to save his friend, while the other will be attempting to avenge his own.
If I had to judge on character, I would say Cap typically has his head on straight, but his number one weakness will always be Bucky Barnes. So long as Bucky is on the line, God only knows what Rogers will do for him. Stark is very similar, but hates betrayal, as seen in Iron Man 2, when Tony shows contempt for Natasha Romanoff AKA Black Widow after he learns that she was a S.H.I.E.L.D. agent, profiling him for Nick Fury's Avenger Initiative, and also in the dialogue above. So the fact that Cap would dump him for a guy who was a supervillain two movies ago will most definitely not sit well with him.
And the winner is... I honestly don't know.
For me, there is honestly no way to choose. But I am curious: who do you want to win?