Australia & America
Legislative Branch Differences
The Australian legislature and executive are fused, whereas these two branches of government are completely separate in the US;
The US legislature (specifically the Senate) has the power to confirm Supreme Court justice nominees, whereas the Australian legislature does not constitutionally have this ability;
Congress has the power to impeach a President, whereas the Queen cannot be removed from office and the GG can only be removed through the Queen (and by convention the PM);
A Presidential veto can be overridden by the US legislature, whereas if the GG or even Queen veto a law, it cannot be directly overridden in Australia; and
Congress - together with the State legislatures - can alter the US Constitution without holding a referendum.
Executive Branch Differences
Responsible government in Australia ensures that the legislative and executive arms of government are fused, whereas in the US the executive is completely separate from the legislature (and, thus, a stronger separation of powers exists);
The US executive is more directly elected (or, at least, the President and Vice-President are) than Australia's political executive, while the latter's constitutional executive is not elected at all;
Elected President in the American Executive government versus a hereditary monarch as Head of State represented by the Governor General in Australia; and
The Australian Cabinet is indirectly elected, whereas the US Cabinet is not.
Judicial Branch Differences
Justices of the Supreme Court of the USA must be nominated by the President and then confirmed by the Senate in order to be appointed. However, in Australia justices of the HC.. are, in reality, simply appointed by the Attorney General (the chief law officer - a member of Cabinet and, therefore, the executive) in a process involving the PM, without requiring parliamentary endorsement or approval.
In America, Supreme court justices are appointed for life, meaning they will serve until death or removed by impeachment. In Australia, Justices of the High Court have an age limit - 70 years old - at which retirement from the Court is required.