This is actually one of the better battles I've seen here in a long time. Bats has the experience but Miles has the raw physical advantage. I'm leaning toward Batman for round one (barely) and Faux Spidey for round two handily.
It still baffles the mind how some of the JL can side with Superman. He is literally killing their former teammates, broke Batman's back and has turned Gotham into a police state...yet they side with him?? Hal and John choosing him (and freakin Sinestro) over the GL Corps is ridiculous.