Yes, I agree Batman is a hard fit in this book. The main problem is that he is seen as so good at what he does it could be Bruce Wayne under there, this Batman has only been around a few weeks according to what we read and yet acts and moves like he's been doing it for years. If he's that good then it's near to impossible to expect him to be any sort of a team player and take a backseat while the novice Alan Scott leads the charge.
I don't understand why they made him such a xerox of the Bruce Wayne Batman though, is there a hidden aspect to him perhaps? Could be be prone to extremes for example? One thing James Robinson hasn't touched on so far is the effect a War has on people, how it can harden attitudes and makes them more prone to casual violence and rage in the aftermath. Actually that's partly untrue - Terry Sloan's actions are exactly what I'm describing. His gradual ability to rationalise extreme action and harsh measures to 'save' society. This Batman could be an interesting tweak on the original if we see how the scale of death in the War, and what it's done to Gotham, has hardened this man to the point he's struggling to find a moral center.
He can act like an urban guerilla, but who it it he's fighting for exactly...?
I thought Rex Tyler was the new Batman?