I've flown both AA F and BA F (though not as an award ticket) and I would say BA F is worth the fuel surcharge. Do an all partner award (if available) ATL-LHR(BA)-FCO(BA)-CDG(IB via MAD)-ORD(BA via LHR)-HNL(AA)-ATL(AA via ORD or DFW). That should still come in under the mileage cap and satisfy all rules, plus give you the r/t to HI that was previously discussed. Or if you want to judge the AA F product for yourself then do the return CDG-ORD on AA (nonstop to try their J on the 763 or via LHR to try F on the 777, which I'd do), though you won't get the BA CCR in LHR, definitely a nice perk ^.