Air NZ have daily flights on both routes - NZ1/2 via LAX and NZ38/39 via HKG (both currently 744s) - so you can take your pick (pricing may differ, of course)! Currently NZ1 leaves mid-afternoon and gets in at 6am, NZ38 leaves mid-evening and arrives mid-morning (however, these timings will be significantly different in July, with the 2-hour difference in daylight saving times).
There's also a good Cathay connection (90 mins in HKG), which is just as quick - CX250+CX117.