How Strong is Batman?

This question came up as I drove to the airport to pick up my mother. Since the WB took Spiderman off the air, Bella and I have discovered the new show Batman: The Brave and the Bold show on Cartoon Network. It’s cool. It’s got a retro-superhero vibe to it and is brighter and more fun than the other Batman shows. So we were watching it last night on the DVR and as we were driving, Bella said “Batman is really strong.”
“Yes, he is really strong.”
“Is he stronger than you?”
“Yes, I believe Batman is stronger than me.” No sense in lying. Eventually she would probably figure out that Batman was stronger than me. So I posed my own question: “You know who is stronger than Batman?”
“Who?”
“Superman.”
We then proceeded to talk about all of the things Superman could pick up, from her baby brother to a building. Finally she asked if Superman was strong enough to pick up the whole world. I said no, but he could fly really fast backwards around the whole world and turn back time. I think that’s where I lost her. That’s okay. One heroic deed at a time.

So I’m slowly introducing her to the DC Universe, and she now knows Green Arrow and Blue Beetle. Although Blue Beetle is really annoying.

I anticipate I will be asked the ultimately question very soon: Who would win in a fight, Batman or Superman? That is a discussion for another day and has been raging for nerd-years. Superman is stronger, but Batman always has Kryptonite with him. Yet Superman knows Batman has Kryptonite with him… etc. But I’m looking forward to it. Frankly, I’m curious to hear my four year old’s insight on this.