jj863 - Welcome to FlyerTalk!
If you are no already a member of BA's Executive Club, you cannot join until you make one flight in full-fare economy (or higher):
http://www.britishairways.com/travel...g/public/en_us
Once a member, you only earn fractional points for most discounted economy fares:
http://www.britishairways.com/travel...s/public/en_us
On AA, there are no joining restructions and you receive full mileage credit for each mile flown.
Plus, if you are not already hold elite status on AA, signing up for a gold challenge will bring you 2/3 of the way towards AAdvantage Gold status (a wealth of information on challenges is available in the AA forum).