While Australia is awesome, how much exploring will you do if you're working the whole time? Just the weekends? Just the city? How much of the continent? There are some amazing sites to see in Australia. But like Europe, most of the cities don't look much different than here until you get out into the landscape.
Now if you are full timing and not working, that sounds like the more enjoyable option, IMO.
I'm not really one that likes to move.
It's probably easier to travel and enjoy the sights here, than it is to uproot your life and hope you have a good adventure.
Playing the devils advocate I know.
Good luck whatever decision you make.