Award availability may be different on each FFP, especially for own metal but also other partner metal.

Award rules are definitely different on each FFP (so some may require most direct routing +/- % mileage while others are strict zone based and others only allow certain number of flights, etc).

Award costs are also different on each FFP.

As for NZ airpoints, I think you are misunderstanding slightly. The 1 airbuck (airpoint dollar) is good for 1 dollar fare only applies to awards solely on NZ metal. For partner awards (or awards that include a mixture of Air NZ + partners), the award cost is fixed. NZ also has some fixed cost awards on NZ metal (longhaul business class).