Looking on airnewzealand.co.nz, it looks like they fly from Heathrow to Wellington, connecting in Auckland, through both LAX and Hong Kong.
I would stick with Air NZ if you can, since they're one of the few airlines that also flies from Auckland to Wellington, and changing airlines in one trip always seems to increases the chances of baggage getting lost, delays causing missed connections, etc. For me, I also enjoy getting a taste of NZ while I'm traveling -- it makes the flight a little more fun.
It looks like the flight through HK is actually 3 hours shorter, so that seems like the way to go. However, don't let people scare you away from LAX -- it's not that bad for an all-international flight, particularly if you're staying on the same airline.
Those flights are 27 hours long all together. Ugh! At least there's something to look forward to when you arrive....
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