While it often makes sense to credit one's alliance (oneworld, Star Alliance, Sky Team) flights to the airline one flies the most, there can be exceptions to that, depending on what one values most in an FFP. For example, status with BAEC will afford one lounge access when traveling domestically on AA; even AA EXP status does not offer that. But award-flight redemptions booked with BAEC Avios can cost more (or less) than the same award flights booked with AAdvantage miles.

You really need to carefully consider what you want out of an FFP, how likely you are to actually get what you want, and what your intended redemptions are. It's a tricky business.