It was established in BvS that Batman has been at it for twenty years. He didn't start out as a brutalizer. And the death of Robin (Jason Todd) was one of the most significant moments in Batman's history.

Superman is an alien of seemingly unlimited power, so accusing the film of xenophobia feels kinda hollow. The battle with Zod caused massive collateral damage. The MCU retxonned Age of Ultron to steal DoJ's premise for their terrible version of Civil War. Also, if you watch the far superior Ultimate edition, it's revealed that some of the more extreme things that Batman is accused of had been orchestrated by Lex Luthor to turn the public against him, just as he was doing to Superman