If you use a lot of services from the rtw desk when you plan your OWE - getting them to help you with rules, etc - and are comfortable with AA, then you probably should continue with them. The BA office in Montreal (?) seems okay but I get the impression they have been well trained but not all of them have decades of experience.

If you know what you're doing and just need someone to make the bookings for you, BA will do a fine job.

Whether you start with BA or AA, when you contact Cairo to take over issuing of the tix you'll be dealing with a set of strangers and afaik on your own to resolve any issues of rules and pricing, should they arise. The North American folks will essentially have "thrown it over the wall" to the foreign rate desk, quite unlike when they do the whole thing in their own office and handle the interface to their own rate desk for you.

If you don't need the domestic AA rtw desk to help with bookings, the decision on who to use to ticket in Cairo boils down to payment, process, and comfort level.

If you go with BA you deal directly with the airline, and pay them by credit card. The downside is that their CAI office does a lot of stuff by hand, and you may need to cajole Ms. Sobhi to give you a tax calculation, if you think you need it. You'll have to personally pick up your tix in Cairo, probably the day before your flight out (although an early morning pickup at ATO is probably okay). Your tickets will probably not be issued more than a couple of weeks before travel.

If you go with AA, you're dealing with an agent. Perhaps AA will stand 100% behind them, but I don't know that. One FT'er who's done that could not use a credit card, but ymmv. But the tickets apparently are machine-printed with taxes shown, and may be issued well in advance of travel, an attractive feature if you're worried about future price fluctuations.