Entirely depends on how good your local post office are. Here in the UK, delivering to my parents out in the country Royal Mail is great. Delivering to my flat in the city, I'd rather have UPS.
Those acronyms mean different things in the US.
USPS = United States Postal Service, the official one.
UPS = United Parcel Service, a different company
I think the parent meant USPS shipments always gets delivered by Australia Post (that's how USPS usually does deliveries in other countries: they use that country's official service), whereas UPS gets their packages delivered by an assortment of local carriers.
USPS -> Australia Post means that I can get the parcel sent directly to my parcel locker [1] and get an SMS when the parcel arrives. I don't need to be present.
UPS -> ??? means I'm guessing whether it'll be a local courier who has the contract or whether it'll be one of the many Toll [2] subsidiaries. No couriers are accepted into parcel lockers (unless you get a Toll parcel dropped off at a news agent).