Miles aren't an issue in this case.

I agree with christep. Also, have you looked at schedules of the flights? Unless I am reading incorrectly, it appears that there is only one flight that would allow you to connect on JL to Singapore. And it has a brutal connection and doesn't get you into SIN until the middle of the night. Just looking at a random day, CX had five valid connections, ranging from morning to night flights, and all had tolerable connection times. This alone would lead me towards CX. I have taken both these flights and they are fine. I can't recall if I have been in the NBC (I think so) but for such short flights all the CX seats I have been on have been fine. Just try to get the 747 or 333 for the nicer biz seats.