Here's the animated movie based on The Tower of Babel (seriously folks, check it out

).
I don't know about a rough and tumble

, but I once said this to [MENTION=12130]Snare[/MENTION], the whole Bats vs Supes debate is really a thought experiment that really could swing either way but it really comes to a battle of two superheroes who happen to be best friends and happen to know each other better than any other superhero or villain. Any generic "who would win in a fight?" argument ignores the character traits that make them who they are. So that raises the question of what the terms and condition of the fight are, has supes gone rogue (a reason Bats has contingencies for him)? Has bats gone rogue? Is Supes going all out (in Hush mind control plays a role so he's holding back, noted by bats himself and even there with a Kryptonite ring he mentions that the last punch he dishes out could break his own bones)? Is Bats going all out (Looking at Tower of Babel, he could very indeed neutralize the entirety of the JL)? The list goes on and includes scenarios that ignore their characters completely (not powers or strengths).
But because I'm all about canon, I'll say this Supes could take down Bats if he was a different character with different motivations, but he isn't, and Bats isn't a different character. It really all boils down to this quote from Bats in the Hush storyline, "I know that Superman could squash me like bug. But I know he won't. Because deep down Clark is a good person. And deep down I'm not."
So Superman has the capability to take down Bats but he never will, whereas Bats doesn't have the same inhibitions.