AA J on th 77W, which is what they fly between LAX and HKG, has a phenomenal hard product. This flight also has enhanced catering, mattress pads, and pajamas in J. The hard product on the AA 77W blows what DL offers out of the water. I bet it's nicer than the J product on JL, as well. Can't comment on BR, as I've never flown it. The only equivalent hard product is on CX, but they don't have mattress pads and all that.
Honestly, CX has downgraded catering so I don't think that is as much of an issue. I've flown the DFW-HKG flights in J, and I find the catering adequate to good. It should be better now on the LAX-HKG flight (at least AA touted it).
My misconnect experiences on AA have been subpar, but if you have travel insurance as a credit card benefit this becomes less of an issue.
I'd recommend AA. IMHO, the only real competitor here is CX. Do you have any status with AA/oneworld?