I have, and use, both right and left side rigs. I prefer both bag and horn on the same side, and since I shoot off the right shoulder prefer my bag and horn on the left. That way seems much quieter, since I usually carry my rifle in my right hand...it’s not clunking against the rest of my gear. But hey, at the end of the day no one is trying to take my scalp, so just do whatever makes sense to YOU.
Greg