Taking your LAX-HKG example, how much are the taxes/fees for a CX award ticket in C? In F?
If using AA miles, the taxes/fees should be identical in all service classes and AA does not collect YQ for award redemptions. (BTW, it's possible that there are exceptions to both of these rules, but I've never encountered any.)
The only case I think think of where premium awards entail higher taxes are flights to/from LHR because they have a luxury tax there.