I wear mine on the right and am right handed.
Always seemed the easiest for me to work from and wasn't "in the way" when loading.
My patch knife which is high on the strap is more convenient, powder measure easier to fill and so on as I work predominantly with my right hand while my rifle/fusil is on the left side
By the way my powder horn I use most and is attached to my bag strap is a left hand horn so go figure!!
Guess I am a wee bit mixed up!!