If a fellow alien can resist the effects of Darkseids Omega Beams, Im sure the actual Anti Monitor can resist them. And the Omega Beams are Darkseids most powerful attack and a mere alien resisted it! Darkseid cant even warp reality for crying out loud. He cant even destroy a universe
I think Frank would have to stay away (Gambit can charge inorganic matter, after all) and use his machine guns and explosive weapons, but these weapons are far faster than Gambit can throw. The Punisher wins.