NZ is considerably cheaper than most of Hawaii and much less crowded. If you go rent a campervan there are tons of holiday parks in beautiful locations and you can also be quite private if you go to the more remote parts such as the west coast of the south island -- where the glaciers are. Really quite different experiences particularly if by Hawaii you mean HNL. Both are good for a honeymoon so you can't make a bad choice, but I find NZ much better. And while I love Australia, most Aussies that I know will go to NZ for their honeymoon

unless they can afford Lord Howe Island. NZ is a pretty special part of the world if you want unspoiled nature.