Both Rogers and Stark were wrong in different ways. Their disposition in Civil War are, I think, a reflection of their past experiences. In Avengers, Rogers fully trusts Fury and criticizes Stark for not adhering to the mission. Stark goes against authority multiple times. Post Age of Ultron and Winter Soldier, we see the roles reversed. Stark is more in line with rules and regulations as a result of the guilt stemming from Ultron. Rogers is more resistant to a central authority.
I don't blame Tony for doing what he did. He's obviously broken over shouldering the guilt of Ultron, dealing with the breakup with Pepper, and the fact that most of his friends are against him now. I don't think it's quite fair to use Spider-Man as a point against Tony. I doubt the writers really even thought of Spider-Man as a criticism against Stark. They just wanted Spider-Man in the airport fight, so they had Tony get him. I don't think the point of that scene was to show that Tony is irresponsible and selfish. And I don't really think it was a huge deal that he wanted to keep Wanda indoors. He wanted to protect her, and he did it the only way he knew how, much like some parents. Maybe the method was wrong, but the intentions were good.
Similarly, I don't blame Rogers for protecting Bucky. After all, he's the last remaining remnant of Cap's time. He was right to go to Bucky before the others found him. It was hard to sympathize with him at the end, though. Even at the airport scene, when Stark was clearly just distressed and desperate, Cap actually told Tony he was the one who broke up the Avengers by signing the Accords. That was a rather shitty way of talking to someone who was supposed to be your friend. He put all the blame for what had happened on Tony when they both are at fault. And he totally lied to Tony about his parents, too. And used the shield Howard made to defend his killer. I would have liked Bucky to acknowledge the murder a little more, at least. The whole "I remember all of them" was a good start, but nothing came out of that. He didn't really seem to feel any remorse and just depended on Cap to bail him out.
Cap's letter to Tony at the end did gain back some of the respect I lost for him, but I can't help but feel that Tony just got the short end of the stick this whole movie.