If considering QF or BA:

On the LHR-SYD run, I'd opt for the longest leg into SYD and the shortest leg ex LHR. This is to maximise sleep if the SYD arrival is in the morning (as per most flights into SYD. QF fits this criteria pretty well. BA is the opposite.

To fly (BA) SIN-SYD with a morning SYD arrival makes for a very long SYD arrival day - and very little sleep hours on the aircraft. The (QF) DXB-SYD sector makes far more sense to me.