Batman from the modern (since '86) comics vs Batman from the Nolanverse?

Christian Bale's Batman vs Bruce Wayne in the comics between the Crisis on Infinite Earths and Final Crisis. Most DC readers should have heard about Final Crisis! My opinion is that Bat-Bale would be about like the Reaper, but that the more experienced Batman would put up a real fight against Bat-Bale. Not sure who would win, though.