For the purpose of this debate, assume these are the two models of being a republic that Australia could adopt.
A Direct Election Model for a head of state in an Australian Republic would involve the head of state being chosen directly by a vote of the electorate.
A Bi-Partisan Appointment Model for a head of state in an Australian Republic would involve the nomination of individuals for the role of President, with a final candidate agreed to by the Prime Minister and the Leader of the Opposition, and confirmed with a 2/3 majority vote of a joint sitting of Federal Parliament.