Australian cities on average aren't much denser than American if at all. Look at Perth for example, it sprawls like a Miami for the population. All the major Aus cities have healthy and active downtowns though.
But with Melbourne and Sydney perhaps there's a case that the way the suburbs are built are somewhat different. Syd and Melb have large and old suburban rail networks that allowed development to focus along the rail corridors. As a result there's a particular pattern you can see around the suburbs of Syd and Melb:
Suburban commercial development is concentrated heavily around railway stations. For example take a look at this suburb in Sydney:
https://www.google.com/maps/@-33.791...!1e3?entry=ttu
You can see the low density housing all around the area, but right in the middle there's a large concentration of shops and some office buildings, anchored by a train station within it, and that serves as the hub for the suburb. If you go into street view you'll see it's a very tight and walkable space with a pedestrian mall in the middle.
And this pattern of development is typical for a large part of suburban Sydney and Melbourne - low density SFH suburbs, anchored by some sort of town centre with a train station in the middle. In the case of Sydney there was also a push to locate suburban shopping malls within those town centres. So most of the major malls there are integrated into those areas with active street frontages, as opposed to being segregated from its environment like how you might picture a typical suburban mall.
So if you take a closer look around the suburbs of Sydney and Melbourne, you'll find a lot less of those gigantic parking lots eating up acres of space than you might expect. (Especially Sydney where the large scale parking lot, strip mall format almost doesn't exist until you reach the outer suburbs)
This pattern doesn't exist that much outside of Sydney and Melbourne though. Brisbane, Perth and Adelaide are mostly "strip mall, big box" suburbs.