We just completed our move from Santiago, Chile to Auckland. We used Atlas International who packed and shipped from Santiago and they subcontracted delivery and unpacking to Conroy Removals in Auckland. Everything arrived in good shape except a few broken glasses. A 20ft container for our 3 bedroom apartment cost $7k US including insurance.
We have visited NZ many times and estimated to furnish a 3 bedroom place from scratch would cost $50k NZ, so we figured it was worth it. Plus we had things like art and rugs we wanted to bring anyway. With the voltage being the same we were able to bring our electrical goods.
Atlas gave us a 5 page list of dos and donts for Customs, including instructions for autos, boats, guns, pets etc. None of which applied to us. Our shipment was cleared by Customs on the high seas before it landed. Not everyone is so lucky!