These two zoos are probably the outsider and the rank outsiders of the group, respectively, which means winning this one really matters quite a lot. The topic? Asia.
The species lists for Taronga, and it is unfortunately pretty weak: Mammals: Asian Elephant Himalayan Tahr Francois' Langur White-cheeked Gibbon Sumatran Tiger Fishing Cat Sun Bear Small-clawed Otter Binturong Red Panda Birds: I'm not sure exactly what they have but there are very few Asian birds in Australia so if Taronga does have any it would be less than a handful of species. Reptiles: Chinese Three-striped Box Turtle Elongated Tortoise Philippine Sailfin Lizard Reticulated Python Monocled Cobra
I was going to look at that a bit later (I'm off to work in half an hour, so it'll have to wait). But they recently opened a Sumatran Tiger area which takes up a large area covering several tiger enclosures, "Asian village" theming, etc. Because a number of their "drawcard animals" are the Asian ones (tiger, elephant, etc) their enclosures do form dominant parts of the zoo. There is also the conservation angle (many ZAA zoos do conservation work in or with respect to Asia, because of the region of the world we are in).
Having visited Vienna barely 2 weeks ago, I feel like I can give a decent overview for the zoo. Starting from the Neptune entrance, there's a large paddock for Indian rhinoceros, nilgai, Vietnamese sika deer and blackbuck. For Indian rhinoceroses, this is possibly the best enclosure I've seen in any city zoo, maybe ever. The Rainforest House has mostly Asian/Indonesian species so I'm not entirely sure what species count here - but most occur west of the Wallace line as well. Highlights here are huge amounts of Oriental white-eye and blue-crowned hanging-parrot, but also northern river terrapin, rock frogs (Staurois parvus and guttatus), 2 flying fox species and orange-bellied leafbirds. Important here is the incredible work Vienna has done with the two Staurois species - they were the first to import them to zoos, and to breed them too. IIRC they do some in-situ conservation with the terrapins too, but I don't recall what exactly. Amur tigers and Amur leopards have a large aviary, which looked well-planted. We didn't take a good look at the outside enclosure because they're pretty common so maybe someone can confirm that these enclosures are indeed appropriate for these species? Giant pandas have what is possibly the best outdoor enclosure I've ever seen for them. Lots of foliage and climbing space. The Aquarium-Terrarium House has few Asian species, but I saw Chinese crocodile lizards, tentacled snakes and spectacled cobra. There's a few other Asian species throughout the zoo - Himalayan tahr, lar gibbon and Sumatran orangutan most notably, all in good-to-great exhibits. The Desert House outside the zoo contains Kaiser's newts and long-eared hedgehog, but both of these are kept in a rather barebones enclosure. (Does this count for the challenge? It costs extra to enter but is jointly managed by the Tiergarten and the Schönbrunn park botanical department)
It is worth noting that the Ectotherm team in Vienna is also breeding a large amount of anphibians and reptiles behind the scenes. Some of the rarities are on show, but the Earless monitor lizards and many others are not.
Somehow I don't think Taronga is going to win this one, but nevertheless here are some photos for interest's sake. Most of the exhibit photos are close to a decade old though. There aren't really any good photos of the elephant exhibit; this one is from 2011: Fishing Cat exhibit (photo from 2012) - note for the Europeans, this is an outside enclosure not some fancy indoor rainforest as you may imagine it to be from the photo: Small-clawed Otter exhibit (photo from 2012): White-cheeked Gibbon exhibit (Photo from 2012): Sun Bear exhibit (photo from 2011): Himalayan Tahr exhibit (photo from 2007 - I think this is a protected structure and cannot be removed): There is a whole thread about the new tiger exhibit area, which can house up to twelve tigers apparently, but seems very poorly executed as a display area: Tiger Trek [Taronga Zoo] I wish Taronga had got Australasia for its category in this round. I'll be voting 2-1 for Vienna.