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].)
[0] https://en.wikipedia.org/wiki/List_of_cities_in_New_Zealand#...
[1] https://en.wikipedia.org/wiki/List_of_United_States_cities_b...