Another interesting dilemma. The best protagonist. Hm...
My go to for this sort of thing would be Krieg, as he's my favorite, but that's mostly because I find him enjoyable and slightly tragic. He's my favorite, but I don't consider him to be the best, as the reason I love him so much is because of the things that he does for me, namely making me laugh with his various spouts of madness in between making the sky red with the blood of those unfortunate or stupid enough to cross his path.
The best, however, is a slightly more complex question. To me, the best protagonist is signified by not only who is established as their own character, but who also makes me understand that despite being the player character, they aren't invincible. That they aren't emotionally detached and need other people around in order to stay sane in this mad, mad world that they inhabit. In my quite limited experience with video games, the character that best fits into these parameters would have to be B.J. Blazkowitz from Wolfenstein: The New Order.
I hate characters who are given gruff or rough voices in a misguided attempt to make them sound badass. But it works for B.J. for one reason only: he isn't spouting stupid one-liners or threatening people or anything like that. A good portion of his dialogue consists of him talking about how tired of this whole affair he really is. How much he hates the war, how badly he wants the fight to be over, and how thoughtful he really is. One of the few characters in a hoo-ah action war game that was made thoughtful and softer, so to speak. (The above term wasn't saying that the game was hoo-ah and the protagonist was thoughtful. I meant to say that the action game was made thoughtful. Spec Ops used to be exactly the same as CoD until The Line came out. Look it up.)