I thought that, as I am voting against the consensus, I would explain my voting a bit here and why I think this match should be much closer than it currently is. I visited both zoos, and I really appreciate what both zoos have to offer in this category.
Let's start with Berlin. The aquarium building is huge, the species diversity (and number of rarities) is brilliant and there are definitely a number of rather good to excellent exhibits to be found, such as the landscape aquaria and the gharial exhibit. So I would not agree with anybody saying that the Berlin exhibits are (mostly) uninspiring or bad (even though I think that there are a couple of enclosures that do not suit their inhabitants well, but these are exceptions rather than the norm). However, for me personally, many of the Berlin exhibits, perfectly good and thoughtfully designed as they are, are a bit repetitive and not necessarily memorable and I do not think that there is any exhibit in this building that I would classify as 'the best of its kind'. I think this is really a matter of personal preference, but I would rather see a smaller number of exhibits that are among the best of their kind. And I think that many will agree with me here that none of Berlin's individual aquarium or terrarium exhibits reach the extreme highs that Burger's Zoo has to offer. However, I do highly appreciate Berlin's emphasis on ectotherms, and the aquarium building is probably the most well-rounded overview of the world's ectotherm fauna and has a rather good overall standard of exhibitry as well.
And that is where Burger's Zoo comes in. Yes, the collection of reptiles and amphibians is much, much smaller than what Berlin has to offer. But I'd argue that most ectotherm exhibits in this zoo are among the best of its kind, if not completely unique. The have only a couple of frog species (White-lipped tree frog and Montserrat whistling frog), but these choice species are held in Burgers' bush, which is (possibly together with some of the other giant tropical halls) the best frog exhibit in the world. The same goes for their free-ranging reptiles in the Bush and Mangrove, such as the Guadeloupe anole, another choice species. Even the side exhibits with the caimans and turtles in the Bush are very good, there are good terraria in the desert for cane toad, gila monsters and red diamond rattlesnake (only found in three European zoos) and the terraria in the Rimba for Asian water monitors and pythons are very large and among the best of their kind.
For invertebrates, Burger's Zoo is (for me personally) the best zoo in the world. There are many insect species in the Bush, (i.e. stingless bees) that play a large role in sustaining the ecodisplay (i.e. pollinating), but they are perhaps not very visible to the usual visitor. However, I do think that they are definitely worth mentioning and I have seen in an educative exhibit in the Safari section of Burgers' Zoo that there is a lot of scientific research going on in the Bush on the staggering invertebrate diversity of the rainforest house. The leaf-cutter ant display in the bush is also probably the best one I know, but still maybe a bit standard and the invertebrate exhibits with cave crickets and tarantulas in the Desert Tunnel section are nicely integrated into the house and well-designed, but also rather standard.
The same cannot be said about the Mangrove, which is probably the main selling point for Burger's Zoo when we are talking invertebrates. The crab enclosure is magnificent and completely unique, with fiddler crabs and horseshoe crabs living in a huge mudflat, that is (as far as I am aware, correct me if I am wrong) self-sustaining. Watching the crabs forage on the beautifully landscaped mudflat is probably the best invertebrate experience I have had. Upside down jellies and a number of fish species, such as four-eyed fish (which are found in Berlin as well in a nice exhibit, but the Burger's Zoo is exhibit is just something else). And let's not forget that the Mangrove is a fantastic butterfly house with a really nice collection of butterflies, one of the best ones I have seen. The architecture of the mangrove in itself and the mudflat is also fantastic in terms of design, sightlines and to me is just a true masterclass of zoo design. I have yet to see another zoo building that places such emphasis on invertebrates and combines this with such innovative, thoughtful and engaging design that represent 'the real thing' for invertebrates so well.
Burger's Mangrove (manatee exhibit) and Burger's bush (caiman exhibit) also hold a good number of freshwater fish species. Especially in the Mangrove, they are a very good sight through the huge viewing window into the manatee tank. The tropical gar in this tank is a choice species that is both impressive and very rare in zoos.
And let's talk about Burgers' Ocean as well. The design here is absolutely inspiring and very well thought out. The 750.000 coral reef is spectacular, the biggest in the world outside of Australia and an example of absolute technical mastery. I personally think that this exhibit alone will inspire the general visitor much more than any of the aquaria in Berlin Zoo. My (non-zoo/wildlife minded family) certainly agrees! The coral diversity (and general invertebrate diversity!) and succes with coral breeding in Burgers' Ocean is also a fantastic achievement worth mentioning. But the Ocean is about much more than just this tank. The first tank you enter is a lagoon tank that is brilliantly designed and the visitor path goes down along it to deeper waters. I really like the diverse species line up here with i.e. wobbegong and guitar rays, but the design and size of the exhibit really stand out. The 'reef canyon' exhibit with morays is also fantastically designed and as a visitor, you really get a feeling of looking into an underwater world instead of an aquarium tank. The completely dark lantern fish exhibit is a simple but (as far as I know) idea that is also very engaging for visitors. The main ocean tank (3 million liters of water) blows the much smaller one in Berlin out of the water, both in terms of size and design. Seeing the huge zebra sharks, grey reef sharks, blacktip sharks, blacktip reef sharks and giant groupers disappear in the seemingly endless tank through the giant viewing window is very impressive. The underwater tunnel with, among others, spotted eagle rays (for which Burger's Zoo is by far the main European breeder) is one of the nicest underwater tunnels I have seen and the fleeting rays above your head are a really nice experience. Burger's Ocean is easily my favorite zoo aquarium and the species diversity is perhaps not on the level of Berlin but I do not think that matters if both zoos have such a great collection. The design, innovation and sheer size and quality of the aquaria are in my opinion far, far superior in Burger's Zoo.
To be honest, it is not particularly close for me. I can think of only a single weakness for Burger's Zoo: their reptile and amphibian collection is not bad, but nowhere as diverse as the collection of Berlin. The exhibits in Arnhem are still second to none, but I would definitely have voted Berlin if it the category was only reptiles and amphibians. But the strengths of Burger's Zoo in the invertebrate and fish categories, both in terms of collection and top-of-the range exhibitry and innovation make this a no-brainer for me. There is no zoo that showcases its ectotherms in such a way. 3-2 Burger's Zoo for me!