In the USA if enter with an ESTA you can stay 90 days but if you have a B1/B2 visa, you can stay 180 days (and have the possibility of extending even that with a I-539 form).
I am a citizen of an EU country and as such I am able to enter New Zealand without a visa. However, I am unable to find how could I stay longer than 90 days -- based on the USA example I was thinking maybe if I got a visa?