British Airways is OneWorld, whereas BMI is StarAlliance. If I were, if possible, I would determine which one serves your destinations better, and focus all the flights possible on that alliance (and preferrable the same carrier).

I don't know about Dubai, etc. but I know that for example Beruit is only served by Royal Jordanian as far as OneWorld partners goes, whereas both BMI and Lufthansa both fly there on *Alliance.

I would make this my primary concern when choosing loyalties, as having an alliance which serves your desinations better/more frequently is the biggest thing in my opinion.