New Catman vs Green Arrow: arrow Catman? I can't say I know a Catman....
The only Catman I know was this lame villain that Green Arrow fought (briefly) in Archer's Quest. He was supposed to help fullfill the Shade's end of a bargain with Ollie to destroy evidence of his crimefighting career in the event of his death (which he kind of blew...). Catman was on the run from that gorilla--not Grodd, the other one--who got him in the end.
Who the "new" Catman might be I have no idea, or if this is even the one you're talking about.
Same guy... he re-invented himself. Currently starring in "Villains United". Basically he's a badass now. Suprised the f*ck out of me, too.