Video by webcamsydney.com camera, plus photos.
Both these ships arrived in Sydney on the morning of Saturday 20 February. P&O's Aurora spent the day at the Overseas Passenger Terminal at Circular Quay, whereas Cunard's Queen Elizabeth spent the day moored at Athol Buoy (which means tendering to shore, but with a wonderful panoramic view of the Sydney Opera House, the City Skyline and the Harbour Bridge).
Early on the Sunday morning they exchanged positions.
They each left port at about 9pm that day, having been two days (one night) in Sydney.