I'm not one of the people you're looking for an answer from and I have very few if any (other than one) qualifications to answer this.
But as someone who has been living in Sydney for the last year and having worked/talked with people across the board from Procter and Gamble, PWC, Electronic Arts, Ubisoft, and a few other big international companies I can honestly say I don't think they care much here. The idea of an MBA is still pretty young here so a good amount of people may not even understand the concept very well and those who have gone are typically alumni of Australian schools (even if they aren't australian).
That being said you can probably see what kind of research you can do with linkedin/school for network of alumni. Obviously I don't expect this to be one of the better answers you get but as someone who's been here for a year I think if nothing else Oxford is a big brand name people will know regardless of their impressions of an MBA education but in the end if you want to work in Australia going to school here will probably be your best bet (I get that may not be an option but worth saying anyway).
Best of luck in your decisions and application!