The mouflons are domestics, so I wouldn't count them and the owl area is a home for kea since a few years, so also uncountable. The only owls on display in Basel are little owls, which are more of an open country species...
So that really leaves very little for Basel. Wild boar, possibly the western gray kangaroo & brush turkey in Australis depending on how you define temperate woodland and then the hellbenders & crocodile lizards...
Artis also doesn't have a lot to offer: red panda, raccoon, striped skunk, red-necked wallaby, Siberian weasel & wolves, as well as a few pheasants, pigeons and crocodile lizards & newts.
Basel offers even less, but has the excellent hellbender display, whereas Artis' strongest one here is the fine Siberian weasel exhibit (an ugly cage from a distance, but a perfectly fine place for the weasels). Overall I will be going 3-2 Artis but it is almost a coin toss.