I use a thumb ring whilst shooting my reproduction Asiatic composite bows. Arrow on the draw hand side of the riser.
Never tried shooting off the other side with a loop, though.
As to the use of the thumb ring, while it takes a while to get the hang of it, when you get a good release going, it works very well.
With the reproduction composite bows, the release I use is a active release, where you push, pull and release, in one fluid motion. Done correctly you get a very clean release, and good arrow flight.