@PAT Zealandia is a predator-fenced valley. All the birds are wild (although the populations of many of the species here are descended from reintroductions from elsewhere), except for the Takahe pair which is captive within a smaller fenced-off section.
@PAT at Zealandia most of the bird species are easy or fairly easy for me to find in a single visit. The main exceptions are the Riflemen which are very tiny and sneaky, and the Morepork and Little Spotted Kiwi which are both nocturnal (there are night tours you can do for these birds).
Around Wellington in general, Tui are very common (I see them every day) and Kaka are quite common (I hear them regularly passing by my house, and I've even seen them in the central city).