(Arguably) the world's oldest zoo was no doubt pleased to draw a strength category in round one, seeing off Edinburgh and Paignton with miscellaneous mammals. They won't be terribly displeased with what Copenhagen has brought to the table either: ectotherms.
I think the main aspects putting Copenhagen above Paris in this match-up are the "Tasmania" and "Tropical Zoo" areas: Copenhagen has probably one of the only (if not the only) large Tasmanian-focused exhibit in European zoos, with devils, grey kangaroos, red-necked wallabies and wombats in modern and attractive enclosures. "Tropical Zoo" focuses on worldwide jungles and includes a large butterfly walkthrough, West African crocodiles, and a variety of well-designed enclosures for fish, reptiles, amphibians, and (if I recall correctly) a few larger inverts. Besides those two exhibits they also have a few enclosures for miscellaneous mammals dotted around the zoo, that all seem adequate for the animals' needs. Paris is interesting because collection-wise it is perhaps slightly superior (definitely in the reptile department, not sure about the mammals), but a lot of the zoo seems fairly mix-matched... The miscellaneous mammals are somewhat randomly dotted around the zoo in exhibits that don't really highlight them or make them memorable (though seeing quolls in daylight is fairly unique). The reptiles are spread between two reptile houses that have a lot of species, but most of those are in enclosures that seem barely large enough, or enclosures that just aren't very attractive. My vote definitely goes to Copenhagen here. I thoroughly enjoyed my visits to both zoos, but in this category Copenhagen should definitely win.
Copenhagen also has some nice exhibits for brown rats and Egyptian fruit bats in their night house, in case that might swing people's opinions. Just too bad for the misc. mammals category that their night house - with a mind-blowing collection of three species - isn't anywhere near Frankfurt/Antwerp/Berlin/Riga levels. I haven't visited Paris, and I haven't actually seen Copenhagen's Tasmania area yet, but going by what I know about Paris (many quite old exhibits and, as mentioned above, some weird mismatching), I'll still let the wombats/devils and the tropical house's ectotherm department - which is not huge or fancy, but reasonably well-done - win here. But I'm not sure if I'd call it a landslide. Both zoos seem to be on a medium tier in both categories where they won't stand a chance against the top guns of Europe, but aren't completely rudimentary either.