That's pretty much it... from LAX, which airline would you recommend?

oops, from LAX to NZ, which airline would you recommend?

Flown them both. Take your pick. Not a shred of difference between them.
John

Both are similar good quality, both are head and shoulders above the average US based airline.

Differences to consider: Qantas has individual entertainment in the seatbacks with something like six movie selections, tv shows, flight path, etc. ANZ didn't the last time we flew them - just the main movie screen. That may have changed in the last 2 years.

Also consider if you're in a frequent flyer program. Qantas is in the OneWorld program and a partner of American Airlines (a consideration for me, as AA is the predominate choice in my area and therefore where my miles are accumulating, plus I like flying them). AirNZ is a Star Alliance member, partnered with United and US Air.

It's a lot of miles not to effectively get credit for.

Actually, the USAir FF program offers mileage accrual and awards redemption on Qantas. The program is not partnered with Star Alliance, though USAir miles can be used on United and, soon, on Lufthansa.