Agree with above about maximizing your segements if you are after more miles.

Why not dfw-jfk-lax in the last part and sample AA's F transcon product and get some more miles along the way?

As far as CX vs. BA? Obvioulsy you would need to add another segement to get you back to HKG to do CX (which then max's out the Asia sectors).

You could do a search in various forum about this one and get a lot of different answers. I really like CX in F the service and meals are fabulous.

Why not go with CX as you will be flying long haul with BA to YVR from LHR. You can then tell us which is better in your trip report

Just to throw another spanner (wrench) in the works. You could always try QF from either SIN or HKG as well. They are getting some pretty good write ups as well on various threads.

If you are stopping over in LHR then one thing to consider is with BA & QF in F you will get access to the BA arrivals lounge at LHR. CX doesn't offer this type of facility at LHR