Superman is the strategist and has the charisma that holds the team together/garners public support. That's why he's at the "center" of the Justice League and the Trinity.
Batman is the tactician and detective whose suspicions protect the teams from the shadows. He's Superman's main advisor.
People follow Superman out of love/inspiration. People listen to Batman out of fear/respect.
Batman is an ineffectual, self-proclaimed leader who isn't taken seriously by the others. He just gives motivational speeches to the other characters who can save the day on their own.