Catman was pretty lame and with time he got lamer, fat and bloated. Then he went to Africa, lived with a pride of Lions and got super-buff and awesome. Now he's a match for Batman in h/h and he gets all the ladies.
That's right kids, all you need to do is live with Lions for a few years to turn your life around!
Anyhow I think in pure h/h Cat and Bat could pull a few wins, maybe even get a split with Deathstroke at his best. Against lower end Deathstroke they take a majority.