Note that you will probably not get F on SIN-HKG, but rather a regional plane with outdated J seats 2x3x2. You will also have to get up extremely early SIN time. With jet lag, it will seem like time to go to bed in UK.
Personally I am not a fan of 13hrs daytime flights. CX F is nice but 13 hours in your cubicle is long, especially if you have flown F before. By the time you get into the plane and get your lunch, it will be morning UK time. Personally, I would prefer flying back from SIN nonstop on BA F; even if CX F is quite superior to BA F.

To get back to your question CX J or F: CX F is far superior to BA F because of the suite which takes the space of 1.5 BA F seat and the great AVOD. To me, food and wines are comparable; service is inferior on BA when F is full because they get so many F seats. CX J is not superior to BA J on the upper deck (actually I find it inferior). On CX J, you get the same huge screen (almost same size) and AVOD as in CX F, but the space is quite narrow compared to CX F; and that is bad for a daytime flight. The new CX J seat are better for daytime. If awards are available, I would MUCH prefer a nonstop SIN-LHR on BA J than a long SIN-HKG-LHR on CX J. But that's me and BA flights must be full with F1.