The subcomponents don't seem far out except in two cases.
Heritage ranks Australia slightly ahead of New Zealand in labour market freedom. I'm pretty sure that doesn't accurately reflect things. New Zealand likely had the world's most free labour market subsequent to the Employment Contracts Act; we slid back a bit with the Employment Relations Act but things here remain remarkably clean. Contrast with the Australia's Fair Pay Commission.
The labor freedom component is a quantitative measure that looks into various aspects of the legal and regulatory framework of a country’s labor market. It provides cross-country data on regulations concerning minimum wages; laws inhibiting layoffs; severance requirements; and measurable regulatory burdens on hiring, hours, and so on.I'm not sure that many NZ union leaders would reckon that New Zealand offers unions a more hospitable environment than Oz; Australian minimum wages are higher and more complicated; the general labour market approach seems far more prescriptive.
Heritage also puts Australia a bit ahead of New Zealand on trade freedom. Australia last year suffered a banana crisis when its banana-growing regions suffered crop failure and Australian "we'll pretend it's phytosanitary but it's really protectionism [see also apples]" regs bit hard; banana prices hit $13/kg.
NZ takes a deserved hit for having allowed the size of government to ratchet upwards substantially under Helen Clark, but we ought to have been credited for our rather better performance on these two measures.