Not sure what your btravel dates are but QF and BA have the same fare on 747 or A380 in June. There are dates when the difference is substantial however that is due demand not fare differentiation. The issue ex the UK is the woeful value of the pound and the extraordinary value Australians are getting when here. QF flights into Europe are very very busy and filled with Australians. BA on the other hand is not getting as much of this traffic as their frequent flier programme does not run in OZ. As a result locals travel with their national carrier.
SIN in 50mins is a breeze incluidng bags. I would not let that put you off.
Your departure point also plays a part. EY will almost ceratinly offer a car to and from airport on departure and arrival and your flight will be 1 stop. BA do not offer cars and you need to stop twice including a T5 T3 transfer and all the risks that that involves.
BA is good but not that good and so I would opt for FRA AUH SYD on EY.