Tony also had the issue that he felt guilty over his failed plan to protect the world that was pretty authoritarian.
I don't think cap would have been against all oversight, but the one presented was very narrow minded and slow to act until more drastic decisions had to be made, like nuking New York.
Kind of what the whole thing in civil war was. Tony was looking to absolve his guilt over the people they failed to save while looking for more and more authoritarian methods of keeping the world "safe".
Cap was much more for freedom and while the idea that the avengers should have absolutely no oversight is absurd, the question of who should be the oversight was important and much of what the avengers did could not wait on a committee to decide to act (also, the last time a committee did act they decided to nuke New York)
True, but GUN in general is just shown as a really incompetent group. The weird general could have been the only one preventing them from going full antagonist against sonic.