Air New Zealand doesn't use either, they use there own system called Carina.

You should be able to check-in online on the Air New Zealand website for the NZ flight number sectors, provided you have got the PNR from Air New Zealand. You're Air New Zealand PNR will always end with H.

If connecting to Air New Zealand from another airline, they should be able to check you in online depending on there system.

I recently flew Swiss/Air New Zealand on FCO-ZHR-PVG-AKL and Swiss was able to online check me into AKL.

Note that in the transit point NZ will make you have you're boarding pass re-issued, and if you don't do so they will probably page you to the gate for this to be done.