Sort of depends... I have a Howard Hill back quiver made in stiff leather. It is my freight hauler as it will carry plenty of arrows for stumping or small game hunting. If I move too fast, arrows will rattle in it, though. This is not a problem when hunting from a stand as I hang it from side of my ladder. I have another leather back quiver of latigo that is not very stiff, and it flattens tightly against my back. It is much quieter when stalking. Both of these require a lot of movement to draw another arrow.
I tried out and like the Safari Tuff but have never actually hunted with it. The idea of a cover to protect fletching is desirable, especially when it is raining. It seems easy to remove an arrow without much movement. It is definitely on my wish list.