NZ hands down.

Food and service are a step up from AC, as are the lounges on both sides of the Pacific. I like the NZ IFE better as well - it's on door-to-door and you don't have to sit through Amex ads before your movie (which is absurd in J).

FYI, there is no AC service to MEL so you'll have to change carriers in SYD. There's also a terminal change, which involves a shuttle bus that is free only for QF passengers IIRC. You may also have to check in again, unless AC can somehow interline you and your baggage. Contrast this to a seamless connection experience in AKL where NZ has its hub and flagship lounge. I'd argue the convenience puts NZ ahead if nothing else.

Other alternatives from NYC would be CX via HKG or SQ via SIN, though I don't know how the pricing compares.