Earning AA miles depends on the route that you are flying. The allowed routes are listed here.
http://www.aa.com/i18n/AAdvantage/ea...es/jetBlue.jsp
Not sure if you can earn on both programs if you hypothetically flew STI-BOS-SFO (earn B6 points on STI-BOS and AA miles on BOS-SFO. I see you have DR where you are from so I gave an example
To be safe I would just apply everything to TrueBlue unless the AA miles would make or break you obtaining elite status.
EDIT: Here's what you can earn on TrueBlue for AA operated Transatlantic, TransPacific, and Deep South America flights from BOS/JFK
https://trueblue.jetblue.com/web/trueblue/aa