Although AA is my primary FF program, I was wondering whether I should sign up for another carrier's FF plan for a LONE4 trip that I will be doing next year. That itinerary includes CX, JL & BA and for most FF plans that I have seen, BA credits only 25% mileage for L class & JL credits only 70% in L class.

Could someone suggest another FF program where (a) I could earn a higher rate than 25% on BA and/or 70% on JL and (b) where redemption does not cost an arm and a leg (in miles or cash) - keeping in mind that all flown miles will be in L class.