If you’re driving, Chemnitz and Leipzig are only about an hour apart. It is, therefore, possible to do both in a day, especially when Chemnitz is a zoo that can be comfortably seen in about three hours. However, I can’t imagine that Leipzig would ever fit happily into a two-zoo-day, even on a return visit.
Chemnitz is actually a three zoo town (almost): there’s a small Wildpark - nothing remarkable but very nice (this may even have 24 hour access). There’s also a small but interesting zoo at Limbach Oberfrohna - certainly worth seeing.
If you’re prepared to pop over the border, Chomutov is only an hour away, and is a pretty interesting place (European species in a large park, with a few traditional zoo enclosures as well).
Or, if you bypass Leipzig, Halle is only a little further north, and could be comfortably seen in a shorter period of time. Not perfect, but a very charming zoo in many ways.