Puh-leaze, I've never figured Batman really put much effort in catching Catwoman. Their "fights" were more like physical flirting. Besides, how many other Gotham City criminals does Batman regularly ally with, get kissed by, and allow to depart on their merry way. She's even helped out the JLA on a few occasions with a whole lot less suspicion than Huntress endured (Case in point the JLA/Titans mini-series). Batman shows the same effort that most Champions heroes show in apprehending Foxbat.
Victory goes to Black Cat all the way.