Zambonir, the obvious caveat to any comparative analysis here is the vast differences in the size and density of the populations. Obviously, Australian officials and politicians have managed the pandemic differently to many of their US counterparts. However, in Australia, there is definitely more public support for government intervention than there is in the US, as well as much more respect and trust in medical authorities.
The libertarian bloc that appears to me particularly vocal and influential in the US is marginalised in Australia. It exists, but has little to no influence upon public policy. Although they (and the anti-vaxxers) have received some coverage on TV news (apparently) and in the online news media (which I do peruse), they did not greatly influence the response to COVID-19. Rather, it has been the small business community which has been most vocal in calling for the re-opening of the domestic economy.
Australian health officials did well to prepare the country for the arrival of COVID-19 and successfully manage the quarantine of travellers from overseas; however, policy implementation has not been flawless. The Twitter thread highlights the confusion over the use of masks in Australia. We've been informed time and again by Commonwealth and State public health officials that it is more important to stay home and, if we need to go out, maintain social distancing (1.5m in Australia). Only over the past few days, with the spike in infections and hospitalisations in Victoria, have officials 'encouraged' or 'urged' the use of masks.
If you followed the thread to another concerned with the lock-down of public housing tower blocks in Melbourne, you can see evidence of a knee-jerk reaction rather than a well thought out plan. Politicians and officials have for months emphasised the likelihood of a second-wave of COVID-19 - yet, when it happened, they behaved in a manner that can only be described as unprepared and callous. I have no problem with lock-downs; however, the lock-down in Flemington seemed particularly 'selective' and sudden. The tenants had no idea that they were about to be confined to their apartments, when the police and medical personnel arrived. Fortunately, support services are now in place for those remaining in what's being termed as a 'hard lock-down'.
Nonetheless, Commonwealth and State leaders (of both both major parties) have enjoyed the support of the vast majority Australians who endured what was, compared to parts of Europe, just a partial lock-down. Yes, some returning travellers resented quarantine and the hotel rooms didn't meet their expectations. However, their complaints - voiced on social media - were met with only a modicum of sympathy, some derision and a general shrug of 'get over it'. Personally, I could not have been happier when the WA Premier enforced quarantine measures, closed the border to interstate tourists and restricted movement around the State.
The pandemic has highlighted significant deficiencies in both countries. Fortunately, Australia's deficiencies have not undermined a concerted approach to saving lives. Unfortunately, America's deficiencies (as outlined in detail by other posters) have produced what seem like fifty-one ineffective, irresponsible and heartless responses, and led to the unnecessary hospitalisation and deaths of far too many people. My wife and I may shake our heads at the latest mass shooting or Twitter-storm by the President, but . . . jeez, this is suffering on a grand scale. Worst of all, I can't even foresee any significant change for the better even after a vaccine is developed. 
