If this is round trip, I would personally fly BA LHR-PHX and fly AA on the return. Reason being that BA 288 PHX-LHR is usually delayed due to a lack of staff on the part of BA contractors. My last two experiences on BA288 were both delayed due to a lack of cleaning staff with one further delayed due to short staffing by ground handlers. My other issue with BA288 is that I have never been able to use the contracted Escape Lounge which is directly next to the BA gate due to it being filled up almost immediately after check in opens. When this happens they redirect you to a significantly inferior Admirals Club which is in a different pier of the B gates.