You will need to go through transfer security to move from arrival level to departure level. There a re a couple of such transit points.
Then, check the gate where your flight departs and go to a lounge near your transit point or near your departing gate.
There are three CX business class lounges (Wing, Pier, Deck) and the QF lounge (near Deck). There is no BA lounge.
All lounges are nice. If convenient QF lounge maybe the nicest.business lounge. But service depends on the time of the day. If near a QF departing flight, they will actively serve all kinds of food, including on trolleys and a la carte. Service is lesser outside of QF flights hours.