It doesn't matter at all for mileage earning whether you book through aa.com, jal.com, or a 3rd party site (in most cases). What matters is whether you book an AA code or JL code. AA codeshare on JL flights earn LPs per AA rules, so 11x dollar spend on base fare if EXP. JL coded flights earn based on the table linked above. For many JL tickets, earning is going to be better on the AA code, but availability is often limited.