To the OP:
It sounds like you won't fly enough to really benefit from CX's elite status system (which regardless is harder to earn than US carriers), so I think you should definitely credit your CX flights to your AAdvantage program.

It also sounds like you might be flying Y more often than J or F - if that's the case, be aware that CX uses a shell-type seat in Y (it can't recline into the person behind you, instead it slides forward). Read some reviews here on FT (there have been countless threads about the "new economy class" or "new y class"), and maybe check out CX's website. It sounds like a lot of people complain about them, although a few (short) friends of mine like them more than traditional seats.

Re fares, haven't checked lately, but I suspect UA is going to match CX for fares now that ORD is coming online...I have to imagine UA fares are going to come down on that route.