Benefit of EK , is that it is a single aeroplane service all the way from DXB to AKL whereas with Qantas, you will have to swap in MEL or SYD to a 737 service for the trans tasman service

Nicer trans-tasman aeroplane ( and I prefer EK over QF for the long flight too ) plus no risk of misconnecting in Australia should the flight ex DXB be delayed would make EK a better choice than QF to NZ

If looking at possibility of using a QF codeshare on EK, QF has no codeshare all the way to New Zealand, only to Australia