Mwenenzi

AA & BA are both Oneworld & freq flyer partners. Award availability at the low "saver" is nominally the same, but in practice does not always happen.
BA has high cash surcharges on awards. AA does not have award carrier imposed surcharges, unless it on a BA flight. AA has "anytime" awards at much higher miles costs.

Having multiple ffp’s with low balances is never a good idea. You may never get enough ff miles/points to be of use before they expire. FFP’s are for the medium to long term. However at times it makes sense to have a ff membership with an airline in another alliance. (e.g. Oneworld & Star)
Be mindful of expiry http://www.flyertalk.com/forum/miles...-t-expire.html

Freq Flyer Award assistance tools
Use at your own risk. (These are not recommendations)
These links give a guide of ff miles needed. These may not be up to date.
Availability is from the airline ffp web sites/phone.
Award flights are never guaranteed. You need to be flexible with date and route.
Frequent flyer miles/points are not equal to or burn. They are not 1 to 1
If a multi segment award check the rules/cost carefully. With some ffp’s it can be 2 or more awards or cost more ff miles/points than a direct flight.
If the award is on partner airline it may cost more miles/points than an award on the ffp airline.
Some awards/airlines/routes can have cash surcharges, in addition to real taxes.
Real taxes/regulatory fees are the same for all airlines on the same route/class.
Some carrier imposed surcharges can trigger additional real taxes when the flight changes from non-revenue to revenue.
-AwardAce: Compare Award Redemptions Across Airlines In Seconds --> http://www.awardace.com/ Has surcharge indication
-Economical Excursionist's Tools to compare Frequent Flyer Mile Redemptions --> http://www.flyermiler.com/
-http://www.flyertalk.com/forum/trave...ast-miles.html --> http://www.awardhacker.com/