Both zoos have remarkable elephant houses in terms of architecture. But in Budapest that is where it stops and even though they have a second house, their elephant enclosure is still subpar.
Beautiful design of the old elephant house (common hippo on the left)
Elephant stable in old house
New elephant stable
Some other pictures:
Siberian tiger enclosure (1 of 2)
Orang utan indoor enclosure (1 of 2)
Orang utan outdoor enclosure
Taking & Visayan warty pig enclosure
Indoor enclosure of Javan langur
Dhole enclosure
Overall Budapest has quite a varied Asian collection, but many of the enclosures are tight on space.
And here is Copenhagen:
Part of the giant panda enclosure
Malayan tapir enclosure
elevated walkway for the red panda
Asian small-clawed otter enclosure
Lesser mousedeer and Bali mynah exhibit
Siberian tiger exhibit
Harbour seal & reindeer enclosure
Musk ox enclosure
One of 2 Amur leopard cages
Asian elephant indoor enclosure
Asian elephant outdoor enclosure
Copenhagen also has quite a varied collection, but in quite some cases enclosures are on the small side, or simply too small. I still would put them ahead of Budapest, but not by much. But if someone can make a convincing argument for Budapest, I could still change my mind.