One downside of BA is their seating policy (although maybe UA is just as bad these days).
IIRC, for BA, assuming you are not an elite FF, you have to pay for seat assignments, except that families can get free seat assignments 3 days before the flight and anyone can get free seat assignments 1 day before the flight. I have no idea whether families ever have a problem sitting together if they wait for the free seat assignment (the people at flyertalk might, although they tend to be more FF elite and not economy).