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Cars are similarly priced and both have similar low mileage. Corolla is NZ new and is 1 owner, the Vitz is an import - just arrived.
Which car is the better bet reliability wise?

You're not really comparing apples with apples. The Corolla is a bigger car with a bigger engine, so perhaps might have longer long-term lasting qualities, however they both enjoy a good reputation for reliability.
Some import Vitz models have a CVT transmission, and if this is the case, I'd go for the Corolla with a 4 speed auto.
Personally, I always prefer a NZ New vehicle with a known history - especially a 1 owner car and I prefer the size of a Corolla, but it depends which type of car suits your needs.