Can, worms, open.
I'd much rather fly direct unless I really needed the SCs. QF would be my choice for superior service and F&B. I also find the Skybeds v comfy even though they're sloped, and generally sleep v well on them.
You'd get New Gen Club World on BA as BKK-SYD is operated by a 744. Very nice seats, far better than any of the other J options. BA service is let down by inconsistency - crew on BA are super on a good day, but can be downright awful on a bad day. The catering is ok, not much flair. Same Charles Heidsieck NV as QF in J for the most part, though some routes now feature Ayala Brut Majeur (yum! Had it on LHR-BAH-DOH return. I'd fly BA just for the Ayala if I can be assured that it'd be served on my flight!), Lanson NV (decent), or Cattier NV (I'd rather drink cat piss). Far prefer the all Australian wine list on QF, YMMV. I think it's been reported on mFT that Lanson has been making the rounds on the Asian sectors.
I do not like the long haul Business Class seats on CX or JL - it is too narrow on CX, and hard as nails on JL. I find JL's J seats even slopier than the Skybeds. I find the CX herringbone v narrow even though I'm not a v big person by any measure - on a JFK-HKG I only managed 2 hrs' sleep. CX should've simply licensed the VS herringbones like NZ which are far superior. I also do not like the cold and haughty style of service on CX and JL - again YMMV.
(Though some of the Senior Pursers on CX, especially the ones from The Phillippines or Sri Lanka, can be rather cool and affable.) CX's catering is ok, again not much flair, and the mains are served on caseroles which feel v mass market. I enjoy Japanese food and used to love the Japanese catering on JL, but now my shellfish allergy forces me to choose the Western options which are yuck. Wine list on both nothing to shout about, unless you enjoy sake and plum wine in which case a wide selection is offered on JL. Most importantly, I believe JL serves Piper Heidsieck NV in J (cheap!), on CX you'll get Billecart Salmon NV (another one of my faves) on all shorthaul routes except Japan and Deutz on other routes including Japan (paint stripper). edit: from memory I think i also got the Deutz on an ICN sector, remember being disappointed as I was looking forward to the Billecart.
Shorthaul on both CX and JL are pretty good, much better than QF domestic for sure, you get a lot more food and there's a full wine list. I believe BKK-NRT is operated by a 767, a long flight in a regional service IMO.