In the comics it was a pretty compelling debate. Revealing all the secret identities could make things safer for civilians, but could also make things more dangerous for heroes and their loved ones. Both sides made legitimate points.
This movie, however, just looks like Iron Man saying "maybe we can't handle everything ourselves, let's work with the government" and Cap saying "I'm going to fight everyone for the sake of my homicidal childhood friend."
I like that the movie version of Ironman is being driven by his fear of what S.W. showed him, and that's why he is all on board for being "put in check" but I have to side with Cap on this one. As he said, "The punishment should follow the crime."
I'm going to have see the movie first, since Cap's motives seem to be driven a little bit differently then the comic book. Cap's judgment may be personally compromised with Bucky playing a factor in this version.