I think it is very telling that Steve talks about trusting individuals and them not letting him down so far. But people let Tony down all the time.
If you really look at the movies, it is always institutions that betray Steve (the US government to some extant in the first movie, Shield is the second, and the UN here). However Tony has always had both the money and the power (in the the form of his company and his genius) so he can't be betrayed by institutions because he knows there is always a way around what ever they have done to you if you have money and power and the patience it takes to use them. Hence his saying we can change the Accords later, because he knows that he can get it changed by virtue of what he, himself, and the Avengers collectively, mean to the world, they just have to appease the public at this moment. I mean he kept Sam and Steve out of trouble for the first bit of their helping Bucky in Romania so there was wiggle room. The current Accords are just an over reaction to some things that have gone down, but things can eventually be calmed down and the contingemcies get worked out. Like he and Natasha point out, it is happening whether they want it or not so might as well get in and change what they can.
While Steve gets betrayed by institutions, people are always betraying Tony, starting with Stane in the first movie. Even in this movie he gets betrayed to some extant by both Natasha and Steve. I mean he is betrayed by Captain America! He can't even trust the worlds paragon of virtue. So it's no wonder he trusts institutions over individuals. He won't be blindsided by what institutions do to him, and he knows he can always find away around them eventually. But people, he let's people down and they let him down. I would be surprised if Tony truly trusted another individual besides Rhodey ever again (and even Rhodey betrayed him somewhat in Iron Man 2, but there were extenuating circumstances that I am sure Tony forgave).
I think Steve would have gone as far as he did for anyone he sees as family, but I think it would have been with more consideration of the consequences for anyone else. With Bucky there just is no thought, there is just nothing he wouldn't do and no one he wouldn't go through for Bucky.