My take is to bank them with AAdvantage cos as long as you have some sort of activity over 18 months, your miles won't expire.

H on JL earns you 70% only. But you can also earn status miles when you fly with Alaska Airlines.

If you fly more on CX in the future, then make sure you buy H class and above, as these are the only fare classes that you can earn AAdvantage miles on.

And when you make elite status, ie Gold - which you may get with a 'challenge' .. you will earn bonus miles with AA, CX, RJ, LA, QF flights.

More on this can be found at the AA forum.