If you can facilitate an internal transfer, that might make the first year or so easy for you (relo costs, visa help etc) + you presumably get to maintain some semblance of a network inside your firm).
A lot depends on what you do - if you are used to managing large SI teams, then some of those firms just don't really do that (e.g. Deloitte).
Bear in mind most people answer these questions in a manner strongly clouded by their own personal experiences/bias, for example putting PWC second, erm, under what criteria? Deloitte do have a good rep tho.
And again, put any two people from a given firm in a room and i'll wager they have different takes on salary/ work-life balance etc. it is very difficult to generalise.
IBM are supposedly terrible at recruitment, they push towards online channels but anecdotally i understand they are impossible to get in touch with other than by channels they don't bother answering.
If you do IT strategy etc, Deloitte or Acn. If you do SI work, ACN or IBM, perhaps Cap Gem or some of the others.
Worth looking at some fo the local players such as Oakton as well.
Which city do you want to go over to as well, may make a difference.
Also might depend on what industry you specialise in.
check out mycareer.com.au and seek.com.au for a flavour of what is around (and the main players own recruitment pages). recruitment consultants can vary widely in terms of quality and knowledge as well, so make sure you check out a few if you go down that route.