Bronx has markhor, tahr, kea, dholes, tufted deer, and various pheasantsm, (and skunk), which Zurich don't, whereas Zurich has Koala (and rainbow lorikeets), as well as the parakeet-squirrel-partridge aviary (and the SA camelids). The outdoor aviaries at Bronx appear more focused on large birds of prey (notably: condor) , whereas Zurich's are more focused on smaller birds, vultures, owls. Bronx has brown bear wheras Zurich has Mongolian wolf. Bronx imo has a clear though not huge lead in species diversity.
On the other hand, where the zoos overlap in species (snow leopard, gelada & friends, tiger, red panda), notably in the marquee exhibits for the first two species, I equally see Zurich with a clear though not huge lead in exhibitry - especially with the geladas, where Zurich's enclosure appears to offer much more structure, vegetation, and climbing opportunities.
It's very close imo, but I think ultimately the kea tip me towards Bronx.