Two hulking beasts with mommy issues go to battle.
Batman would clearly win, because winning is what he does, but I wonder if he'd consider Jason to be human or not. Jason is like Solomon Grundy in that he's not technically alive, so Batman probably wouldn't have a problem using lethal force.
Based on his abysmal fights in that trilogy I doubt it.
But,
I’ll give you the benefit of the doubt. Miracles happen.
Fights here don’t generally work by one character getting to use every piece of equipment they’ve ever used in order to win/not get machete’d in the face.
Adam West would definitely have something in his belt to take out a zombie.
First of all, I don't even agree that Baleman is an abysmal fighter, but that's entirely beside the point. He's still a lot better than Jason is in the first four movies, who while incredibly strong and durable for a standard human being showed zero in the way of defending himself. If teenage girls with no martial arts can defeat Mama's Boy Jason, he would get his ever loving ass kicked by Bruce.
This isn't a Versus match though, it's a scenario where Jason is in Gotham killing people. Once Bruce realizes that Jason is an inhuman monster, he'll have no problem blowing him into pieces with the batmobile.
I'm not sure why you're trying to accomplish here.
Baleman loses against other superheroes and comic book characters because his universe is grounded in reality compared to the ridiculousness of the MCU or DCEU. However, he's more than capable of doing well against conventional action and horror movie characters like Jason Voorheees.