I prefer the service on CX, and the seats are comfy enough. You might be lucky enough to bag some of the new CX herringbone flat beds in J. Agree with Captain on the BA hard product, but two drawbacks: DFW goes into LGW, and then you'd have to haul over to LHR (allow 4 hrs!), and you would lose out on the trans-atlantic mileage. A more varied itinerary could be something like DFW-MIA on AA and then via MAD with IB (necessitating a change in LON as well) or even more freaky DFW-JFK on AA, then using AY via HEL. Personally, for mileage and ease, I'd take CX first, JL second, then BA third (if mileage accrual is of concern to you).