I will quote from the B777 FCTM and I think it will answer your question at the same time.
"If a missed approach is required at any time while circling, make a climbing turn in the shortest distance toward the landing runway. This may result in a turn greater than 180 degrees to intercept the missed approach course. Continue the turn until established on a intercept heading to the missed approach course corressponding to the instrument approach that was just flown. Maintain the missed approach flap setting until close in maneuvering speed is completed".
So I believe the answer is that you would do the MAP procedure for the approach that took you to the MDA in the first place unless instructed otherwise by ATC.
