For the longest time, I only had the first half of this crossover. Great art and interesting story set-up.
I always regarded that it wasn't that Dr. Mid-Nite was the Earth-2 equivalent of Batman but that since he had no counterpart on Earth-1, the closest counterpart to Dr. Mid-Nite on Earth-1 was Batman. It's kind of fitting in a roundabout way as Mid-nite's origin and concept is that of the pulp's Black Bat: Man blinded by acid during a trial gains the ability to see in the dark but keeps on pretending to be blind. It's the origin of Two-Face as well though the outcome is different, scarring on half of his face instead of losing his sight.
Ah, that's classic, isn't it?, having to wait for yonks for the conclusion of a vital concluding chapter!