I realize I am kind of late to the discussion and I doubt I can sway anyone. Anyway. So far I have only voted in competitions where I have not visited both zoos, if I felt one zoo does something in the particular category so exceptionally well that it merits my vote nonetheless. In this case, I have only visited Vienna.
The project of modernizing Schönbrunn zoo must have seemed a nightmare at the outset: a zoo grounds going back more than two centuries under - I'm sure - very strict heritage protection. How could you possibly succeed? In contrast, on visiting the zoo I was left with the impression that renovating the zoo must have been a delight. Not only did Vienna succeed in this endeavor exceptionally well, but they also did so while preserving the zoo's heritage both physically and 'in spirit'. This is a very rare feat, illustrated by countless (i.e. virtually all other) zoos that either preserve the original zoo grounds but fail or fall short in moving their exhibits to a 21st century standard, or demolish and rebuild large parts of the original zoo grounds from scratch sacrificing much of their heritage, or expand the original zoo grounds or open up a second location altogether. In this sense, Vienna is unique and it imo shows most in their bird, carnivore, and primate exhibits.
Doé's primate exhibits look perfectly fine (or better), but I have not found any evidence that they constitute something truly exceptional (such as their aviary) as Vienna's imo do.
So my vote goes to Vienna.