What makes the Winter Soldier such a formidable adversary for Captain America?
He is a direct problem for Steve Rogers' psyche because of who he used to represent to him. He's a good adversary, because he plays into Steve's Achilles' heel. We saw, after the first movie, that Steve Rogers went into this post-traumatic stress-type guilt because he wasn't able to help his best friend. When Steve comes face-to-face with the Winter Soldier, he faces a dilemma within himself that he's partially responsible for. That's already a weak point for Steve.
He adds of the Winter Soldier's decision not to let Captain America die, "That's why he doesn't kill him. That's why he saves him. That end scene to me was always like: 'I don't know what this is, I just know I'm supposed to do this right now. Whatever this is, I'm supposed to protect this for some reason. There's something about it that's unexplored, and I'm going to figure it out.' And that's kind of where he's at at the end of the movie. It's not like he's going, 'Captain, Steve, let me take you out of the water,' you know what I mean?"