If you are travelling direct (I'd advise it, otherwise you'll backtrack 6-7 hrs crossing the Tasman) you'll end up going either OneWorld(Qantas LAX-SYD, SYD-AKL, AKL-LAX) or StarAlliance (UA LAX-SYD, NZ SYD-AKL, NZ AKL-LAX). I only fly C, I found NZ & QF matched in food, quality of service, and with the new VOD entertainment as well. UA, not so much.