When I shot recurves, I sometimes used a bow quiver, but with longbows it just seems to mess up the balance. Also, there is a whole lot of visible movement when using a bow quiver. Plus, back in my foolish youth, I had one of the bow quivers that did not cover the broad head. Yep, stabbed myself in the thigh, but luckily not seriously. That's when I gave up the bow quiver.
On the other hand, a back quiver is sometimes noisy and prone to hang up in brush. Note: if your back quiver rattles a lot, you are moving too fast. Also, my back quiver is my freight hauler. I carry extra items attached to it or in the storage area, which I can't do with a bow-mounted quiver.
I don't see myself ever going back to a bow mounted quiver, but you will find many effective hunters who love them. My suggestion is try them both and use whichever one suits you better.