I did a comparison for all (major) destinations departing from Sydney using MR points. We now get 1.6x more Asiamiles or Qantas points than AA points for each MR point.
While AA requires fewer miles than CX in almost all cases except for economy class to Asia, taking into account that we get 1.6x more Asiamiles than AA miles changes the picture quite a bit. There are now only three regions where it requires less MR points when transfering to AA instead of CX: North China, Middle America and Middle East in Business or First class. For all other classes and destinations, the required amount of CX miles is less than 1.6x the required amount in AA miles.
Of course this does not take into account that AA usually charges much less fees than CX, but only compares the required points.
There is not a single class or destination where QF miles are better than CX miles. For most economy class destinations it is better to use QF than AA, but for anything else AA is much better than QF. I did not find an MH chart, so cannot compare it.