I've never been to NZ but the data is utterly against that. The most dense city in NZ (Auckland) has 2418 people/km^2, and Christchurch is about half that. Wellington is 1918. [0]
By contrast every US city in this table [1] is way above that, with the lowest being 3889.4. (New Orleans, surprisingly, is a mere 783 [2].)
That's interesting. I wonder how they calculated the area. There's no way Yonkers is twice as dense as Auckland in a practical sense (I would guess it's similar). As for Wellington, there's a very limited amount of space to build on because of the topography. As a result, houses are small, streets are narrow, cars are small (I had a difficult time driving a tiny hatchback). The CBD is unusually big and dense for a city with a metro population smaller than Madison, Wisconsin. The airport is shoehorned in to the only flat space in the region. So why does it have a low density? I'm assuming undeveloped regions are being counted here. I suspect density in terms of "used space" is quite high. Totally anecdotal obviously.