Television's Biggest Badass Of All Time, Final Round: River Vs. Batman!

River Tam: a child prodigy, subjected to weird brain experiments and turned into an unstoppable killing machine. Who can stand in her way? Maybe the guy who trained since childhood to become the greatest detective and the greatest fighter?

So which Batman is it? It's any version that appeared primarily on TV. That includes the 1960s Adam West Batman, the Batman: TAS version, and the current Brave And The Bold. Plus any others I've forgotten.