I don't understand why they went so convoluted in this, apart from trying to shoehorn The Dark Knight Returns in.
Given the chance to write the BvS script, I'd have doubled down on the Superman as an Act of God vs Bruce as Humanity metaphor. After the destruction of Metropolis, Bruce would have already resented Supes enough anyway, but in my version I would have had him reacting to a couple of big disasters (probably some big supervillain stuff masterminded by Lex Luthor) but in a way that, despite his best efforts, leaves lots of collateral damage and innocents dead.
Bruce decides Supes is a menace and sets out to find ways of stopping him. Lex let it slip that he's recovered some kryptonite from Zod's ship but oh-no, it's been stolen by a B or C-List Batman baddy. Batman stops the baddy, recovers the kryptonite, and then there's one last big super-fight and Bruce resolves to stop Supes, as Lex knew he would.
They get into a fight, Supes tries to explain that he didn't mean for people to die, there's a big argument (intercut with kryptonite punches) where Bruce flat out tells Supes that he's too dangerous to let live. At this point, both of them are on their knees, bleeding and weak, but they begin to understand each other. Bruce begins to see that Supes never meant for anyone to die and Supes realises that in his titanic battles, he hasn't been paying enough attention on the little people caught in the crossfire. (Hey! Character development)
Lex suspected this would happen, so he decides to finish off the weak superheroes himself. Neither is strong enough to beat Lex alone, so they have to learn quickly to work each other's strengths and cover each other's weaknesses to beat Lex.
Blah blah blah, they realise that they could each learn from each other and make a bigger difference to the world together and form the Justice League.
Post Credits sequence: There's a baddy tearing up Metropolis/ Gotham, Supes and Bats arrive together to stop him, but then the smoke and dust clears and the baddy lies beaten on the ground, cut to Wonder Woman all sweaty and battle-scarred. "What took you boys so long?" Or words to that effect.