I think if it's in long haul Y, I would pick BR and CI hands down if I am in CX hard shell seats. If it's short haul Y I would base on price and all 3 will be indifferent.

If it's long haul J then CX will win if I don't value time. If stop-over and time become an issue (cause it does take couple more hours), then BR (for 180 degree seats if available) or CI (for price based). If it's short haul J then time does become more of an issue cause it factors in travel time more, so probably BR or CI over CX unless CX offers a great price to cover the time lost.

If you have to choose a FFP to bank your miles in, check the way you fly and decide yourself... and yeah, do message us and let us know what happened.