If you were rebooked onto a different BA flight that didn't have problems, it would seem that you have no grounds for a complaint against BA.

AA flights FROM the EU are covered by EU 261 but not AA flights TO the EU.

For compensation terms, look at AA's Conditions of Carriage. They must follow their own policies in this matter, but it sounds like you had a mechanical delay and were flown to your destination by AA at the first opportunity for an available AA seat. AA may own you a hotel room and food vouchers, perhaps also a free phone call and transportation between the hotel and airport. They might also give you some customer service "apology" miles but are not required to compensate you in this way.