I can confirm, I moved from Seattle to Sydney. It's not even close.

Single data point on new grad s/w engineer salary at small/medium business in Melbourne, circa 2015 ~40k in USD.

we have generally higher wages and prices on the low end (that is, the rest of the population and high minimum wages), and comparatively lower wages compared to the US coasts for tech/stem. That high minimal wage and remoteness affects the price of a lot of things.

That being said, the original poster is a little bit off, as both Sydney and Melbourne have inner-city transport options and infrastructure that outcompete practically all American cities in that regard, and punches pretty damn well on a worldwide basis (behind only a few cities that are notable specifically because they are world leaders).

You're right that Melbourne and Sydney infrastructure outcompete pretty much all US cities, but the punching above their weight on a worldwide basis is Australian mythology. I've lived on both and several cities in Europe and Melbourne and Sydney are behind pretty much every big city in Europe and Asia. Public transport for example is absolutely atrocious, the state of the roads are extremely poor...

That reminds me of a story. In 2009 I flew into Sydney with a team of 20 people and 40 duffle bags, and the regional airline to Melbourne refused to check half the luggage despite us having a pre-arranged letter from them stating otherwise. So, a team member and I rented a car, bought a SIM card and several Red Bulls, and drove to Melbourne to join the rest of the team the next morning. With the international flight, that was a very long day!