If you are connecting to SYD, then the only real choices are QF F, QF J or BA J - as the QR lounge does not open until around 18.00/18/30 but stays open until around 2am (check timings as the BA flight retimes with daylight saving changes etc. I think QR opens 4 hours before the QR flight - the QR lounge website is generally correct). So you could nip in before the flight for a bit but does not seem worth it to me, other than curiosity. On the return QR is open.
My personal preferred is QR over QF for all the reasons I have said here and in the QF similar thread.
It may not say First but QR is only available to J/F passengers and just wins on every category (food, drinks, seating, restaurant, showers, power sockets etc) - except some people find it a little too empty with a high staff to pax ratio.
The QF lounge IMHO is more of a OWE lounge and an acoustical assault, is very focused on feeding QF pax heading from SIN to AU - with a flight time of around 7 hours is very short so people like to eat and drink in the lounge and then pass out on the plane - which reflects in the cafeteria atmosphere (Not judging, just calling it s as I see it from probably 30+ transits). If you like Singapore tastes then the QF lounge does do a good laksa and the fish is usually very very good. So I will admit that if I doing the BA11 to BA15 I will stop in QF for food and then chill in the BA lounge.

Do one one-way and the other the other way. There are no bad lounges in SIN and each has a differentiator (QR, BA, QF F, QF J). We are just all a bit spoilt....

KF