From the beginning, Cap has not been a good little soldier obeying orders. Rogers was originally told he couldn't be in the army, but he kept going around to different recruitment offices trying to find one that would let him in. After the Super Soldier project was scrapped, Cap was relegated to being a mascot. He still held out hope that he would eventually be given a real assignment, but when he found out Bucky had been captured by the Nazis, he again defied orders to go get him and all the other POWs in the same camp. He was then given the authority to be the one to decide how to take down HYDRA. After being revived in the present, he chafed at going on missions for SHIELD when he didn't know everything that was going on. He openly opposed project Insight as being overreaching. When Fury was taken down, even before he learned it was HYDRA behind the whole thing, he went against SHIELD to find out the truth.
Tony, on the other hand, has been motivated to go to extremes because of guilt from the beginning. In the first Iron Man movie, he's a happy-go-lucky arms dealer until he's brought face-to-face with the death and suffering his company was manufacturing. He then shut down the most profitable aspect of his company and built himself a suit that he could use to take out the terrorists who were using his company's weapons to cause that death and suffering. In Iron Man 2, he was willing to alienate Rhodey and Pepper because he knew he was dying and felt guilty that he'd be leaving them. In Iron Man 3, he issued a challenge to the Mandarin because he felt guilty he hadn't done anything to stop him to that point. After defeating AIM, he destroyed all his suits because he felt guilty about the danger he was putting the people close to him (Pepper and Happy) in. In Avengers 2, he built Ultron because he felt guilty for not having been able to stop the Chitauri before they even got to Earth.
It makes much more sense for Iron Man to take the bleeding heart path to submission than it does for Cap, who has shown he is willing to fight against anyone for what he believes is right.