Well I agree with Planestupid here, there is essentially very little difference between BA F and CX J.
BA F's seat is small in the land of first class seats, and therefore when a seat of similar although slightly smaller dimensions comes along with the CX J seat, with the same shape and similar layout in the aircraft cabin, you have a product which is very similar.
CX J don't have pyjamas. But CX J don't seem to suffer the endless catering shortages of BA F, so you can actually have similar quality food and selection in CX J and BA F too. Plus CX J have their signature drinks which is an additional treat on CX.
You have to mention the service which for most part on CX J is very good and much less variable than BA F which can range from brilliant to bad.
Combine these factors, and you have a similar product with BA F and CX J, for a much lower price on CX.
The BA A380 F seat is huge. The BA F seating density in any comparable cabin (CX don't have new J on the 744 which is the worst BA F cabin)is half that of CX. There is a good amount of personal storage on the floor of the wardrobe and all around the BA F seat. It is easy to have a lot of belongings spread around you in the BA F seat this isn't possible on the CX J. The A380 F seat also has the capacious storage bin between seat and window which doubles as the charging port for USB and laptop power.
BA F doesn't have catering shortages per se, the food upload on a cabin which is lightly loaded has always been low which restricts choice especially in the event of any last minute ticket sales boosting numbers in the cabin. This was always the case with BA even when the F product was far far better than it is today. I agree that BA should look at this but it isn't a comparable position with being on an aircraft with 2 full J cabins with the consequent multiplication of choice from that in a 14 seat F cabin.
As for menus well BA food has not been a strength for a very long time however it is difficult to go by just a menu description. The BA F meals are also served flexibly to meet passenger demand, you can't do this on CX J, the BA meals are hand prepared, the CX J meals are as I understand pre-plated.
BA now I think carry Drambuie in F so you can order a Pacific Sunrise if you like on BA.
I love CX and think that CX J is far better than BA J with more consistent (and generally better barring a stellar BA crew) levels of service. CX F is also leaps and bounds ahead of BA F but I don't think that it is a credible argument to claim that CX J is as good s BA F it really isn't although I am sure for some the difference are small enough to favour CX J. I don't think the differences between the 2 products are small though and as HKG moves to more A380 flights the difference becomes much larger.