He's Batman taken several stages further and without the privileged background. So of course he's methodical. If Batman's energies were directed at hunting and killing criminals, instead of just finding and catching them, and if his heart was completely gone, he'd be Frank. One reason his relationship to Daredevil is interesting is that in some ways, together, they're the ideas in Batman split between two characters. DD believes in justice, Frank retribution. Batman wants retribution but holds himself to justice.
To elaborate on that last thought, a personal analogy. When I look at most serial killers, or rapists, or similar levels of scumbag in real life, my gut wants the death penalty. But I am not a supporter of it. Because regardless of what would satisfy my gut, to me it doesn't change that the state hasn't the right to take a life. What my gut wants can feel right, but still be very wrong. That's why our brains moderate it.
Batman would be a similar case. Whereas Frank dropped that concern, and focuses his brain on the hunt and killing alone, having already accepted the premise that justice doesn't exist. Batman would be more one who believes justice is possible.