Some astonishingly good answers, particularly Ben Kelley and Melodie Neal.
To a European, we are clearly New World, and closer to the US than to Europe, as others have explained. Melbourne is more European (and it has gotten even more European since the 90s, with the promotion of foodie culture and laneway restaurants in the CBD); but that doesn’t make it very European.
We are still a long way from anywhere, and relatively isolated geopolitically if not commercially. Our cityscapes are still spread out and very suburban compared to Europe. We still have a dearth of engaged citizenry and public intellectuals; which is why Waleed Aly is too good for us (and I’m happy he’s gotten himself a commercial infotainment forum). White Australians have an acute dearth of history. Traditional Anglo-Australian (“Aussie”) culture is somewhat on the wane, which is not really a positive development, and likely more a victim of globalisation than of us ethnics.
OTOH: we are not weighed down by history, just like the US isn’t. We still pay some lipservice to egalitarianism; class is emerging (popular derision of “bogans”), but it’s nowhere near as entrenched as it has been in at least some of Europe. We are a placid, confident place to live, though not as placid or confident as we used to be. We are no longer a cultural wasteland. Clive James, bless him, was part of a mass exodus of intellectuals to Britain in the ’60s; he’s recently admitted that they were too stupid to recognise that there was a cultural upsurge happening just as they left, from the new European migrants.
Yes, the majority narrative of why multiculturalism is a good thing stops after “um… cuisine”. And there are clear and pressing problems ongoing with our indigenous community, with the xenophobic mistreatment of asylum seekers, and with the twin problems of the failure to integrate Lebanese Australians better, and the stoking of islamophobia that takes that as a pretext.
On aggregate, I’ll still say, our rendering of multiculturalism has translated into a somewhat less rooted, yet open and resilient society. So far.