When people are going to kill your friend, then yeah... emotion would play into your motivation. Steve was willing to allow Bucky to be taken into custody... he just wasn't willing to allow BUcky to be killed for actons he knows he wasn't really responsible for. But that's Steve.
Though Stark in round 2 was the one acting on emotion when he realized a brainwashed Bucky killed his parents. Again, that's pretty understandable too.