I've never had any Issues flying in/out of CHC with Customs or Biosecurity. I have flown with both SQ & EK.
The short walk within the same terminal on arrival is good.
Having to fly on an ATR back to WLG after arriving on an EK 380 in First is not fun!
On a separate topic: As a Wellingtonian I did enjoy flying in/out of WLG on SQ. I could be home within 30 minutes of arriving.