HBP: Pitcher and Batter both ejected

[AirSocata]

I am inclined to like the idea of making the coach that is complaining the most pick first.

That said, I think the two ways to choose that are fair and removing your discretion which can always be argued against is one to take the "first out, first in" method. If you can not determine who was tossed first, than make them both give you their choices without knowing what the other has chosen and that is what it is.