[MunchkinMan]

To add to the futility of trying to affect the combat, the duplicate would still get updated should someone play a Monster Enhancer on the original still on the Monster side, and the original would get copies of what's played on the duplicate. I'm also of the mindset that if the Monster is cheesed off by (i.e., gets a bonus), or afraid of (i.e., gets a penalty) your Class, that bonus/penalty might still apply to the other Monster. Time to get a second official opinion.

Either way, unless you're very low Level, and have no Items, you're most likely winning the combat, since the Monsters cancel each other out and you still have your own combat strength added to the fight.