Inasmuch as I appreciate AP comments, from what I've seen incoming people do choose our employability but once they've had a good run for a few years here and got their papers sorted they will move over for better long-term careers, social care and employability in Australia. These are those not looking for resources-sector jobs but for regular white collar city jobs. They eventually move to AUS especially if their first language is not English. For migrants the jobs are hard to get in outside Auckland unless one is a UK state sector expat - these folks tend to crop up everywhere in public sector jobs here, but much less so in Australia. This could be because we produce enough our own graduates here to take those jobs, while it may not necessarily be the case across the ditch? I don't know.
And no, I have no no figures or sources to support the above, so for all that I know I may be talking shark.