While BA and AA don't let you earn on each other for trans-Atlantic routes, there is one HUGE benefit to BA Executive Club, although it may not be what you are looking for. BA allows you to pool up to 6 other family members (FF account must have same mailing address) and claim reward based on the sum of those accounts. So, family of 5 makes a trip to Grandma getting 5K miles each, you can claim one free reward ticket based on the 'Household Account' total points.