My limited opinion is that it depends upon whether you are flying alone or with someone. You said "I" have the choice, but then the choice is for the day "we" want to travel.

If you're on your own, I thought JL was better. I liked the seat more (huge!) and the flight attendants were very good. I thought the food was better, but some have said they didn't like the JL choices.

If you're with someone, they don't call the JL seats the "solo" seats for nothing. They are fairly isolated and certainly not conducive to carrying on conversations. BA would be a better choice in that case, imo. Some people have said that BA is faltering a bit, and I admit I haven't flown with them for about three years, but I have always had good experiences overall.