On topic, while they may only have the same level of knowledge as they would as comrade superheroes, Batman is a detective. He'd do extensive research on Spidey, while Spidey would only be able to get the basics. Spidey's well known in New York, he's looked to as an icon. Batman's considered an urban legend by those who've never seen him, and some kind of monster by those who have. Batman's a skilled interrogator and investigator. Spidey's a scientist. Bats has no real weaknesses to exploit. Spidey has superpowers. Spidey may have equal prep, but there's nothing for him to prep AGAINST. How do you prep against boomerangs? Or a grappel gun? Spidey wouldn't have the information on Bats, and wouldn't be able to get it. Bats, on the other hand, will have proportionately much more. So while the fight may drag on as Bats lures the web-head to his trap, Spidey's going down eventually.
couldn't have put it better myself. Batman can hack into city cameras and pull footage on Spidey, analyze his moves/technique, come to the conclusion that Spidey has some sort of precognition ability, see just how fast and strong he is. Hell bats would pick out a suit with increased durability and pack enough gadgets to take on two spidermen. while Spidey will do his own research and prep this is normal morals and Spidey would not go all out on Batman knowing he is just a man without powers and a bunch of doohickeys. Spidey is definitely stronger and more powerful (obviously) but I Pete needs more prep than Bruce. It won't be an easy fight but Bats takes this
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