You don't mention the type and size of the BB you're installing or the brand and model of MB.
So, even though as most of the members here have said Coping "IS" corners provides a superior product long term it does take practice to get good at and when you are adept you'll rarely ever do it different.
Couple stupid questions
1. How high is your MB fence?
2. How high is the BB you're trying to install?
3. Assuming the BB is store bought, is the back side relieved, (material removed to assist in flex roll and uneven wall surfaces)?
If the BB is higher than the MB fence and the back of the BB is relieved it may likely be the relief is in contact with the fence in stead of the nailing plane tilting the BB stock back and over the top of the fence. This would explain the reversal of the error when you flip it.
Rarely is a concrete or wood wall close to perfect, add drywall, plaster/joint compound etc and you have a finish mans horror show. Lastly trim stock right from the lumber yd has too high a moisture content and shrink enough within 6 to 12 months to make one cringe. Coping considerably hides the shrinkage from the average eye. If the finish man is worth his/her salt he knows which side of the joint to cope to hide shrinkage from the eye.
Work smart not hard!
Never bite the hand that looks dirty