This is a very tough round as this plays into the strength of both zoos. If Rotterdam would still have had the Riviera hall (old reptile house), it would have been an easier choice, but alas it hasn't.
Reptiles & amphibians
Singapore Zoo might be one of the best zoos in the world for reptiles, maybe not in absolute numbers, but especially when it comes to turtles and tortoises there is great diversity. Exhibitwise there is not much to complain either with the vast majority kept in spacious and nicely designed terraria or open enclosures. Night Safari has even more Gharials, but not much else in terms of ectotherms than a few petshop species. River Safari has several more reptiles dotted throughout the zoo (another Gharial), but here they are mostly in small terraria.
Rotterdam has seen a vast reduction of their once enormous reptile collection, but is now more limited. There is still a very nice complex for African crocodiles (Slender-snouted & nile) and in the Oceanium, as well as on several other locations in the park good reptile and some amphibian displays also exist. New is the nature conservation center where several (locally) endangered species are kept and bred. But in sheer number they are drowned by Singapore. So final score for this part 2-1 for Singapore
Fish
Both Singapore Zoo and Night Safari have hardly any fish species, so it has to come from River Safari here. Allthough freshwater fish form an important component of this zoo, there is not actually that much diversity and a lot of attention is given to huge fish species. Most impressive are the Mekong giant catfish and Mekong sting-tailed ray. Apart from that it is mainly Alligator gars, Catfish, Arapaima, Arowana and other larger species. Tanks are large, but in total volume eclipsed easily by Rotterdam.
Rotterdam has one of the top aquariums within a zoo. Although the original journey from North Sea to California is not there anymore, in terms of fish there is a lot to love still. There are several large North Sea tanks with a large variety, as well as smaller tanks for smaller species. Then there are a few mediterranean tanks, but the highlight is undoubtedly the Atlantic tunnel, which holds 3 million liters and has a large variety of sharks, as well as large and small fish. Then there are several coral reef tanks, a Mangrove themed tank with a large breeding group of cow-nosed ray as well as other large fish species (some of which very rare in Europe). The Oceanium also has some freshwater species from Central America, as well a new breeding station for small endangered freshwater fish, including some Malagasy species. To finalize there is a large Kelp tank and some smaller tanks with fish from that area. In addition to the Oceanium there are a few fish scattered throughout the zoo grounds, Tiger fish in with the crocodiles, and 2 aquariums in the Asian section, as well as a large pond in the butterfly house with Arapaima and other big S-American fish.
Overall score for fish 2-1 for Rotterdam
Invertebrates
Both zoos have a butterfly house, but the one in Blijdorp is far larger and more attractive. Apart from butterflies invertebrate numbers are somewhat limited in both zoos, with random exhibits located here and there. But Blijdorp has a large coral reef tank as well and more invertebrates in general in the Oceanium (e.g. in the North Sea and Kelp forest tanks), so that is a more easy win for Blijdorp 2-1.
Overall I think Blijdorp edges out on Singapore, despite the fantastic reptile collection and displays in the Zoo. The River Safari just cannot compete with the Oceanium for fish and for invertebrates I would also prefer Rotterdam. So all in all 2-1 for Rotterdam.