Which is better is a matter of opinion, and there are lots of opinions available

. They are different. My opinion regarding some of the differences in the product:
Seat: BA goes to fully horizontal position, while QF is flat but slightly sloping. Some people like to be horizontal while others are comfortable with flat and sloping.
The QF seat is slightly longer and also wider than the BA seat. for example there are 8 abreast on a BA 747 lower deck and 7 abreast on a QF 747 lower deck. But on the upper deck the narrower BA seats leave a wider aisle.
Some people like the BA window seats as they face backwards, while other people do not like facing backwards and find it makes them feel sick. This is a personal issue.
On BA there is nowhere to keep your bottled water which can be a pain on an overnight flight. I find I keep knocking it off the little triangular drinks fold-down tray on the side of the seat. QF's Skybeds have all sorts of storage places, including ones specifically designed for water bottles.
Food: In my experience, QF's catering is of a higher standard than BA in business class. A few years back they were very similar, but BA has gone backwards a little in the last year or two.
Beverages: BA has better scotch, while QF tends to have better wines. All else is much the same.
IFE: BA's screens are on an arm that swings out from the seat, while QF's are mounted in the back of the seat in front (except bulkhead and 747 row 16 exit row). This means the BA screen is more adjustable, but in my experience some of the mounting arms are getting very worn and the screen can tend to flop around and not stay where you want it. You also have to move the screen around to access the meal tray on BA, while on QF the screen is always out of the way of the tray, drinks etc.
QF is steadily introducing Audio and Video On Demand (AVOD) through their 747 fleet (already installed on A330-300 fleet). Some would say that with the poor reliability of the QF AVOD system that may be a bad thing. When it works, AVOD is great, providing a much better choice of material and being able to start, pause and stop as you please rather than having to wait until the next cycle begins.
Service: Can be hit and miss on both airlines. My experience is very similar with both and I have no preference based on service. I fond both to be professional and adequate, with QF generally a little more casual and BA a little more "proper".
Lounges: Identical on the Kangaroo route.
Remember that for travel between UK and Australia, you also have a choice of CX via HKG. Will not be a single flight number, but generally similar pricing and still OneWorld. The CX service is superior to BA and QF. The CX New Business Class seats are more like QF being flat but sloping, but those seats are only on flights to SYD and MEL. CX flights to BNE are on A330 aircraft with their regional business class seats which are not fully flat.