As you have to connect, I would also consider where you have to connect, and what plane you will be on for the non-intercontinental flight. For BA, you would fly IAH-LHR-FCO. As said above, for LHR-FCO you would be in European business which is just regular economy with a seat blocked off. You'd also have to go through security at LHR, which can add hassle to a connection. Also, make sure the plane you would be flying on BA is the one with doors, if that is why you are choosing BA. Not all their planes do, and planes can switch at any time.

Is there any particular reason you only list UA and BA?