You can credit different segments to different FFP's. I am doing this Thursday. You need to be 100% sure the correct freq number is each segment. Keep the boarding pass's until you see the avois/miles in the correct account on line.
Is it BA or CX freq flyer program who has the bonus? No-one can advise you if its better to credit to BA or Asia Miles. Depends what you will do with avois/miles and status. And be careful about avois/miles expiry