I really am torn between 4-1 and 3-2 here. Having not seen Chester's new 'Heart of Africa' in person yet, I will move my vote down to 3-2 until more information about the English collection is provided, but I feel very comfortable at the moment in giving Prague the victory. So far the only arguments but forth in favour of Chester are
@merlin 's criticisms of Prague which mostly strike me as the sort of gripes that anyone naturally develops with their local collection over time (for instance, animals being inactive or not using outdoor areas, interesting statues being removed), bar some valid aesthetic criticisms and the comments about the poor hippo enclosure which are impossible not to agree with, sadly.
Prague has the excellent Africa Up Close pavilion, really engagingly designed and packed with exciting enclosures such as that for Mechow's Mole-rat (just about the only one I've ever seen to provide natural substrate for them to form their own burrows) and Senegal Bushbaby with a large nocturnal space for an enormous troop. The vivariums here are also of an exceptional standard and have some rare and easily overlooked lizards, such as Vaillant's Mabuya. Garnett's Greater Bushbaby, Honey Badger, Bush Hyrax, Black-and-rufous Sengi; just a stunningly good collection.
The savannah is exceptional too. Not sure how it compares to Chester's in size (online tools still show HoA as a construction site, so there's nothing to measure), but aesthetically I think its a lot better, judging HoA from images. The other hoofstock paddocks in this area, for Mhorr and Nile Lechwe, are lovely too, and I like the mature trees in the bongo paddock. Solid Aardvark and dik-dik enclosures, too. I will admit that the hippo enclosure is inexcusable though when considering how recently it was built and how theoretically easy it would be too connect it with the bongo enclosure behind so as to provide them with grass.
I love Dja Reserve, and think the Western Gorilla enclosure there blows the nearest equivalent at Chester (the chimpanzee island) out of the water. The indoor enclosure is massive with a lot of climbing apparatus and substrate for foraging, and the outdoor enclosure is very large, again with good height and some nice landscaping, though it could definitely do with more trees; hopefully this is resolved some time soon. The other enclosures in the building are nice too and have some interesting mixes: RRH with De Brazza's Monkey, Brush-tailed Porcupine with talapoins, Straw-coloured Fruit Bats with Gambian Pouched Rats, all in really solid enclosures. The RRH space is perhaps a little too sparse, but Chester's enclosure for the species is no more or less so; much more indoor space at Prague too, with equal provision of areas to forage. Méfou Centre is another really good gorilla enclosure. The chimpanzee enclosure at Chester has a smaller but better-planted island and a miserable, dark indoor area.
Brown Hyenas are a serious asset for Prague here, as both a species and an enclosure. I think its up there with the best exhibitry that Chester has to offer here; so large, so well-landscaped with the undulations and placement of rocks, dens and bushes offering plenty of privacy even if the hyenas want to move around. There are numerous viewing areas at different angles to allow visitors a strong chance of seeing them but the hyenas can easily evade you should they please. Nearby Addax enclosure is gorgeous as well. And for me the Barbary Sheep and Macaque enclosure is better than
anything Chester has to offer here; not sure I need to explain why this one is so great!
Below the cliff is an excellent hilly Cheetah enclosure, a species that Chester is currently lacking in; viewing is poor, but for the animals this space, especially with the adjacent offshow paddocks, is really good. Nice Fossa enclosure in the feline pavilion, though not comparable to Chester's. In general, Madagascan fauna is one area where I don't think it can be disputed that Chester has the edge. The Sitatunga enclosure on the other hand is an area that Chester can't answer to; they no longer keep the species, which is quite fortunate when one compares their former enclosure to the streams, reeds and swampland of the Prague enclosure, among Europe's best. There are also Cape Fur Seals, a really interesting and attractive pinniped that Chester once again can't really answer to, in a nice enclosure with a great pool.
Moving onto birds, the African aviary in 'Bird Wetlands' is really good, providing a good water feature, areas for perching, solid height and a really good selection of rarities for us: African Openbill, Squacco Heron, Hartlaub's Duck and Red-winged Starling. Much like the hyenas, the Shoebill alone deserve recognition. Their aviaries are so-so, though (the use of live fish too feed them, simulating fishing, is a nice touch), and the big lawn opposite has far too many pinioned birds for my liking. The Ibis Aviary on the other hand is great with Yellow-billed Storks, various waterfowl, doves, owls and vultures all sharing one huge walkthrough space that blends into the cliffside.
Again, its aesthetically superior to any of Chester's aviaries, though definitely smaller than Tsavo or the African Wetlands. There are a few relevant species in the remarkable Great Aviary (the praises of which I've sung enough before). Moving towards the Pheasantry, we cannot overlook the Pel's Fishing-owl, which Prague is the only public collection in the world to have bred, and are of note simply due to their rarity. There are also the likes of Egyptian Vulture, Hooded Vulture, and Madagascar Crested Ibis around here.
There is slightly less on offer with regards to reptiles: I've already mentioned the various really impressive vivariums with some interesting species in AUC. There are Gaboon Vipers and Occelated Skinks in the Feline and Reptile Pavilion. Hingeback Tortoises in Dja and (I think) some relevant species in the Terrarium round off all that is on offer in Prague here.
Overall, my reasons for voting Prague boil down to the following:
1. The best of Prague (cliffside paddock and aviaries) exceed the best of Chester, and in general I'd say that the savannah and the hyena enclosure are also comparable to the best English offerings here.
2. The collection is far more interesting, with more pleasing large mammals (the lack of rhinos certainly compensated for by hippos, fur seals, cheetahs etc), and smaller rarities (bushbabies, the various rodents in AUC, Brown Hyenas), as well as of course birds where the collection is far more novel than Chester's.
3. More interesting and engaging enclosures throughout, with the caveat that I haven't seen HoA in person. I think design-wise, Dja and Africa Up Close are immeasurably more exciting than any of Chester's simply designed paddocks that look at times indistinguishable from those at most British collections.
4. A really impressive breeding record throughout: the owls are a highlight.
I'll give the discussion awhile longer to hopefully bubble along before I provide more comprehensive summary of all that Chester has to offer, make my case for why it merits the win, and hopefully convince both 
