Little difference. Identical lounges at both SIN and LHR (or is the BA arrival lounge access only for QF Platinum and not including F pax?). Similar on-board seat and service (more variation between individual planes than between BA and QF). Food generally better on QF but not a sure thing, similarly wine/spirits better on BA but not always (and QF has recently upgraded its F service, though not clear that it is much of an improvement -- I have yet to try it). BA service is more consistent, but QF crews can be better and almost always more fun (you may or may not like that aspect). I'd pick QF just because I'm bored flying BA (and their F service has gone downhill a lot this year).