It depends on the specific aircraft type. If you can get the TPE-HKG and HKG-SIN segments on aircraft that have long-haul business class (i.e. 744, 74J, 34C, 34D, 346, 333) then I would say definitely go with CX - you get AVOD and the long haul seats.

If you can't get on those flights then it might be a closer call, but even so it's quite a long detour, so unless you need the miles I think I'd still go with CX. The lounge at HKG is better than the one at NRT as well, particularly if you have OW Emerald status and can get into the F lounge.