I'd without a shadow of a doubt go with Emirates on the A380, the cabin pressure difference on the A380 isn't a gimmick IMO, it does make a considerable difference to how you feel after a long flight.
The only way I'd choose the LAX routing with Air NZ would be if you could get a free 24 hour stopover in LAX, at which point it would be a cheap way of breaking up the journey with a night in a hotel.