Regardless of weather it is one or two tickets, one still need to pick up all bags from CHC international and recheck in on NZ. Hence, even if you were flying VA or NZ from CHC into Nelson or another ports, the bags will not be checked right through into NZ. Exception would be if you were traveling the other direction, from domestic airport from NZ connecting to an international destination, then you do not need to pick up your bags.
Flexi ticket is always preferred, it is not so much the 80 or 90 mins on the surface, rather, it is what would happen if the EK flight is delayed. You will have no one to turn to when they are on two separate tickets.