If all of this is on IB metal you get slightly better control of your ticket on IB. IB's IT isn't any more fabulous than BA but if it's booked on IB then it should be easier to get seat selection, and if there are any irrops then IB should be easier to contact. I wouldn't over play it. If you do book on BA, then you can still use the IB app, use the BA PNR and it should convert to the IB's PNR.