Well, if you're trying to fly more direct (I don't think there are non-stops), you don't have many options. Usually if you look at the "most" expensive ticket, you'd be likely to find the "best" as well (cause the market can bear it. Look at LA to HKG-Cathay's first-class is by far most expensive. Wonder why?)
You have many options with a stop. I'd say most people would say:
SQ-great
CX-great, though it may be more variable than SQ (I prefer SQ)
Middle East airlines-they have luxurious new planes, I have never flown them in business but I found their service lacking (compared to the Asian airlines).
JAL-I don't know how their stuff is, they underwent bankruptcy and most people I know fly ANA.