They basically leave and arrive at the same time, so choosing by schedule won't help.
When I did this trip in Y I used to prefer QF 1 through BKK because the first leg was longer than the first leg on QF 31 through SIN. Seemed to break up the trip better. Conversely on the way back I would go through SIN to get the long leg over with, leaving just a (relatively) short hop down to SYD.
In J, though, it would depend on how well you sleep. Taking QF 31 through SIN gives a bigger uninterrupted chunk of sleeping time on the leg into LHR. If you sleep well on planes this could help you to adjust to British time better. If you don't sleep well, you may prefer to go via BKK to make the two legs closer in duration.