With Batman and Superman, it feels like it's the same as the difference between Fashion and Style. Batman is the Fashion hero - he'll come and go with the fads, the tides and always be, well, fashionable. Superman is the Style hero. Styles don't change. Batman is more malleable, Superman is a fixed point.
People like malleable and unpredictable. When Batman shows up, you don't know which version of him you're going to get - growling, antisocial, paranoid, hardass or is it the batman who keeps lollypops in his utility belt for children, teams up with aliens and is fundamentally compassionate/humanist?
When Superman shows up, you know what you're going to get. You know everything is going to be OK. That's part of his appeal. (I do think the character works better when he's reliably rebellious to authority and power structures, but that's a whole other conversation).