Most immigrants living in New Zealand end up staying, So I hear. Some of the South Africans I have met came here with the intention of eventually moving to Australia, and they still here with no further interest in leaving.
But I have not yet heard of a Kiwi not liking Australia, they all seem to love it and speak very highly of it. This is one of the reasons for the huge skills shortage in NZ, many Kiwis move to Australia, its no myth.
With all the rain we have been having here in Wellington, I have actually caught myself now on a few occasions thinking that I may have to give Aus a try. However, I have not been there, except to Sydney and will be there next week for a few days. But I am slowly starting to love this place, who knows what the future holds, have not experienced a NZ summer yet either.