AA has a dedicated RTW desk (phone number is 1-800-247-3247) which is widely regarded to be the best there is. Although occasional reports of spotty service or 'new' people, they know their stuff. I'm not even sure any of the other OW airlines have an equivalent, dedicated group. Booking with AA versus BA is a no-brainer - obviously as an "AA person" I'm biased but I think you'd find most people around here would suggest AA over BA.
I strongly agree that booking with AA versus BA is a no-brainer.