Personally I would take the earlier flight and have a longer connection - but I am very conservative when it comes to connections. Note there is only one daily QF departure to AKL from LAX, so miss it and you lose a day from your vacation.

But I am also basing this on my ability to access either the T4 Flagship Lounge before heading over to TBIT or the new OneWorld F lounge at TBIT for a shower, food and "preparation" for the long flight.