It all depend on what you place the highest priority:

Seat/Bed:
Both have flat beds on this route
QF's seat/bed is wider and longer than BA
BA's seat/bed is horozontal, while QF's is flat at a slight incline

Catering:
QF better for food, especially in J cabin
QF has better wine selection
BA has better Scotch and probably other bar offerings

Lounges:
Exactly the same lounge at both locations

IFE:
Very similar. Look at the airlines web sights for current movies that may appeal to your taste.
QF has larger screen, but further away on the back of the seat in front, unless in row 11, 16 or 23 where it swings up from the armrest. BA screen must be moved to fold out the tray at meal times.

Amenities pack:
Very similar. The current QF one is probably slight advantage, but not difference overall.