If you can't get A380 on Qantas, then definitely BA on 747, try to get the upper deck.

BA fully flat, more private. Qantas Skybed Mk 1 angled-lie flat, so any talk about BA being sloping compared to Qantas on 747 (at the moment) is nonsense.

The only reason to pick Qantas 747 over BA 747 is if you are so big the BA seats feel narrow, but even then, the aisle ones on the new Club World (which is on all 747s and 777s now) are still preferable to sliding down on the Qantas 747.

Of course if you COULD get the brand new CX business class (via HKG) that would be better still, but you don't get it on 747s which operate all but one service into LHR at the moment. The existing herringbone CX business class product is fully lie flat, but by far the narrowest of the OneWorld options available.