"Why Batman doesn't kill?" and "Who would win between Batman and Superman?" are the two proverbial questions about our Caped Crusader. Answers to which are also in the comics, either through clever dialogue or unforgettable imagery. The first question is answered here in Batman: Under the Hood, Vol. 2. 
 Continuing both in tone and story, the second volume of Under the Hood ties up all the loose emotional strings between Bataman and Jason Todd, who was earlier revealed as the one called the Red Hood. This is clearly a definitive Red Hood origin story, both a culmination of the Jason Todd Death in the Family and commencement of the anti-hero Red Hood. 
 Once again, Winick has effectively utilized unknown (at least for me) characters like Captain Nazi and the Hyena in some of the book's action scenes. Count Vertigo was also there, and I have read about him only at Green Arrow. This volume wraps the Black Mask story branch at the middle to give way to the most awkward reunion of all time: Batman, Jason Todd and the Joker. 
 Then the throwdown of fists and philosophies happened between the Batman and the Red Hood. Specifically, Batman answers the question why he doesn't kill, even if the only one he has to kill is the Joker, THE Joker. The answer earned a respectable nod from me, though it is neither the most logical nor the answer which is the best one. But once I felt the gravity of Batman's answer, hell yeah, that's Batman right there. (Opinion: Now, this may be connected why people hate the killer Batffleck in Batman v Superman, but if you just try to understand what Bruce has gone into, plus other considerations, both the logical and rage-driven choice is to kill the Big Blue.) 
 Under the Red Hood (which collects both volumes of Under the Hood) is a must-read modern-era Batman story. It is has well-balanced elements which are effectively executed to deliver a definitive origin of the Red Hood and an answer to Batman's no-kill policy.