It may be awkward and impolitic to suggest, but my experience with BA has always been that behind the scenes (i.e. with baggage handlers) there are many strongly held resentments about anyone being treated better than anyone else....despite (or especially because) the potential beneficiary paid more for the service. Last month I watched bags being loaded onto BA 3 (LCY - JFK) in what appeared to be an abusive, deliberately careless manner, and it took over 45 minutes for the bags of this business-class only flight to appear on the belt at JFK.

Having flown CX F only a half-dozen times, it's obviously not fair to generalize too much ---- but each time our bags were among the first to appear.