CX only recently opened their lounges at LHR and they are modelled (so I read on their website) on the HKG lounges which are superb.
The AA Biz Lounge at LHR is getting very "tired" these days.

I don't think it would matter which card you flashed as long as you are EXP you would get into either. The US seems to be the only place where getting into clubs is a problem (for non-international travel).

I am looking forward to checking out the CX lounge at LHR next week!