Have visited Chester, but not Berlin, although it is probably the zoo I am yet to visit which I feel most well-informed on.
As a whole, Berlin's offerings appeal to me far more than Chester's in this category. Other than RotRA (the best orangutan enclosure that I have seen), their incredible work with Babirusa and the huge hornbill aviary in the elephant house, most of their Asian exhibits left me a little cold (the Eurasian Black Vulture aviary, which counts, was also brilliant, although most of the species are European). Monsoon Forest was closed on my visit, and as a result Islands felt really disjointed, with a lot of backtracking required, and not many animals seen. It also felt as though a lot had been spent on theming, and yet not for a single second was I convinced that I was anywhere other than rural Northern England. My visit was in winter, no doubt playing a part in the vegetation, but it was a very sunny day regardless. Other than that, I liked the new lion enclosure (the theming here struck me as far better-executed than in Islands, perhaps somewhat controversially) and the outdoor elephant enclosure, although I thought the indoors was a little poor, something that I am always surprised not to see other enthusiasts talk about. Most of the Asian hoofstock enclosures throughout were good, but nothing that I hadn't see done very similarly, often better, at most other British zoos; that said, the thick sandy substrate rather than dusty concrete in the Onager and camel enclosure was a nice touch. Dragons in Danger is mostly category species in solid enclosures, and I was pleased to see some nice aviaries for Asian birds throughout (the ones opposite the chimpanzees, for instance).
It is evident that Chester has a lot of real quality in this category, and I have no doubt that the circumstances of my visit are a big reason as to why I didn't take to most of it all too fondly. Aviaries with wave machines and steep, rocky exhibits for mountain bovids are two of my favourite exhibit types, and Berlin has excellent examples of both of them which are certainly on my bucket list. The Asian section of Welt der Vögel looks nicely done and probably has just as many rarities as Chester's various Asian aviaries. I also adore the look of those cattle houses and the fact that within them are both male and female gaur, which is such a hard thing to come by these days. The Aquarium no doubt adds a lot of real interest, too.
For all those above reasons I am really tempted to vote for Berlin here, and have done previously, but have switched my vote to Chester for the same reason that I leaned so heavily against Berlin in the Beauval thread: the Rhino Pagoda, and specifically the fact that some rhinos have to be locked indoors. Why any zoo would knowingly build an enclosure and then proceed to acquire more animals than it can handle without providing any means for separation other than locking an animal indoors is beyond me. The elephant enclosure is also poor and the orangutan one, while not awful, doesn't look great and is far inferior to either of Chester's.
For those reasons I am, very reluctantly, voting 3-2 Chester. Very much open persuasion.