If it's less than $10K NZD (equivalent) you wanting to transfer, then I would just bring it over as cash.
Although 3rd party currency exchange rate companies offer better rates, they're a bit more inconvenient and take longer for the funds to clear. Your $ goes from your US bank to the 3rd party account then to your NZ (BNZ) account. If you frequently transfer $ across, then I think it's worthwhile and it also depends on how much we're dealing with at exchanging.
I like simplicity. If you can negotiate with a currency broker in the US for the best rate, use them to transfer funds to your BNZ account.