With Joint Business fares you can either book the respective business class bucket on the BA coded flight or 'F', 'P', or 'A' on the respective AA coded prime service. Which bucket should be selected for the AA coded flight really depends on the fare rules. In my practice, either 'A', 'P' would do, especially for AA fare. The thing is that there is no set rule - some of the BA's 'R' fares allow booking into 'F' while more expensive 'C' fare only allow booking into 'A'. If you want to get more TPs then go for the AA-coded flight (not possible on ba.com) but the agent will need to play with different booking classes to get the right one (however, there are only 3 and 'F' won't work with 'I' fares anyway).
here are a handful of TransCon flights where there is a business class cabin and you'll be booked into one regardless whether you're booking under BA or AA code.