I'd be thinking along the lines that Bd and Wb quick kill each other in their respective bounds, so the Bd being I generally doesn't matter much - getting the first hit becomes very important and the fight is over quickly.
Ax and Wb don't quick kill each other, so I would expect the fight to be more drawn out.
Also, Ax move more freely, but irreg Bd require two PIPs for anything other than straight ahead. There again, if upgraded to reg, it's easier to get out of the way or stop short or hard flank a Wb column and kill two at a time.
Consequently, I would do some tests/simulations first, then decide which I liked most and base accordingly.
Anthony