Having never visited either collection, I do find myself leaning a little bit more towards Plzen here, which is where I have placed my vote for the time being, but I do feel as though I am somewhat lacking some information.
The design of the Czech River exhibit fascinates me and it is definitely a bucket list exhibit for me. I can't find too much information about it though - is it just for otters and fish, or are there reptiles and waterfowl too? Either way, a big asset for Plzen here, I feel, and it inspires me in a way that the Stuttgart aquarium does not. Speaking from experience, with aquariums such as Antwerp or the former one at London that are from what I can tell similar to Stuttgart, the long series of somewhat repetitive tanks tend to get boring. The law of diminishing returns ensures that by the time I have finished the aquarium I feel indifferent to most of the fish, and I strongly suspect that should I ever visit it myself the same could well apply to Stuttgart.
Some of the tanks in the gallery also strike me as a little cramped and sparse, more so than the Plzen ones. So while I love the large paludariums, overall, I don't feel particularly inspired by the exhibit, nor enthused to see it in person. The contrary is true for Plzen.
I also really like the look of AkvaTera, although it is hard to tell as few of its exhibits are pictured online. Plzen also seems to have a rather extensive waterfowl collection, and whilst I have heard past criticisms about the quality of the aviaries (the depth of the pools for diving ducks in particular), some other aviaries look rather good, and Stuttgart has issues of its own in this category with several pinioned waterfowl; one of which, the Northern Gannet, is living in what is quite possibly the ugliest waterfowl enclosure that I have ever seen. I also really like the way that Plzen seems to integrate fish into other displays, such as the Mediterraneum or 'Underground World.' The latter, much like the Czech River exhibit and several of the aviaries throughout the zoo ground, excite me and make me want to go out of my way to ensure a visit in a way which Stuttgart's offerings here certainly don't.
I understand that many of the reasons above, especially those regarding Stuttgart's aquarium, may come across as quite subjective and opinionated, especially given my rather limited experience having not seen them in person. But as I mentioned at the start of the Cup, my logic for voting in such contests where I haven't visited either is to ask myself which collection I would rather visit for the category? And Plzen is easily ahead of Stuttgart in that regard.
Would be happily proven wrong in any of the above points by someone with first-hand experience of either collection, but there is my current stance on things.