Array determines range, resolution, mutliscan capabilities etc. Software (powered by adequate computing power) not only determines tracking of targets and commanding the planes but also has a hand in resolution, filtering, range, etc.
With computing power rising so fast in last decades, military is hard pressed to keep up. I would expect that wedgetail for australia has actually better capabilities than regular US awacs. Only because it is newer. Any upgraded US awacs will then leapfrog it. And so on. Advanced hawkeye is sure to be more capable than today's E3, for example.
Capability gap is always dependant on a curve. When US made its first awacs and other countries had no awacs, that gap was infinite. Then other countries made their first awacs when US was already modernizing theirs. A gap was always there but it's consequences weren't always the same. As computers take over more and more, govt sponsored apparatus is too slow to react to changes. It always changes in fairly large increments, instead of continuous rise. Furthermore, there is a practical limit of how much more useful it is tracking 100X over X number of targets.
No one is suggesting that US will be matched in tech anytime soon. But it is the nature of the technological development along a curve that signals the gap in practice is getting smaller. It will never be reached without investments bigger than what US has now, but it will get closer.