You really will have to look up the regs or give a call/email to each of the CAAs concerned, it will be the only way to know for sure.
Listening to people here could put you wrong because there are variations of recognition depending on CPL, ATPL, and how many thousands of hours you have.
I would speculate that there must be some sort of dispensation in place for taking on overseas pilots in Australia under the 457 Visa scheme or they wouldn't be able to employ those pilots quick enough if they had to go through that many hoops, compared to if you do it under your own steam.
Also be aware that Australia has a better
recognition of the EASA licence than NZ does.
Despite which licence you may want, work out which licence is easier to get for you, and then use the TTMRA to get the other one.if need be. Note there are far more jobs in Australia than NZ.