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Don’t know about the entrance costs, which surely are available on the web sites for the zoos. I have been to both zoos. Basel’s is quite famous, and a good deal larger than Zürich’s.
The Zürich zoo is rather small, but quite nice. It does not have the variety or size of Basel’s zoo. Of possible interest is the cemetery along the walk from the tram stop to the zoo entrance. Quite beautiful, graves of many famous people, including James Joyce. His statue watches over the grave site.
tripadvisor.com/ Attraction_Review-g188113-d542816-Reviews-James_Joyce _s_Grave-Zurich.html
In Basel a ten minute walk from the train station brings you to the Tinguely Water sculpture. Worth a detour.
myswitzerland.com/en-us/tinguely-fountain-basel.html
There are four trains per hour from Zürich to Basel, with transit times ranging from 53 minute to 1 hr 11 minutes.