I started out with a back quiver because they seemed cool. Then I had two times where I was ducking under a thick branch and had a nock hit and drive a broadhead clean through the bottom of the quiver. Kinda scary walking around not knowing there's a razor sharp broadhead inches away from the back of your butt. Plus the arrows rattled around and my fletch got buggered up. Ya, I know there measures you can take to reduce noise and ways to hang the quiver for clearance but I decided to try a bow quiver.
Got a Selway slide on for my longbow and used it several seasons. I liked it a lot and never had any issues in the tree stand. The arrows actually lay well across my lap and are not wobbly at all. Probably more stable than just the bow as the bow sometimes wants to rock handle downwards and I've dumped an arrow to the ground but all you have to do is hold on to the bow or let a hand rest over the string.
Eventually I tried one of the Side Stalker quivers that Dean Torges used to recommend and it is far and away my favorite way to carry my arrows. Quiet, out of the way, accessible and can be worn while wearing a back pack or carrying a tree stand and you can still get to it just as easy. When you have to get on hands and knees to crawl through the thick stuff, a quick wrap of the strap around the bottom of the quiver shortens things up so the quiver rides close and out of the way.
When I'm in the tree, I just pass the quiver strap up under the safety strap I'm hooked to and tie one half hitch and the quiver hangs beside the trunk and again, arrows are nicely accessible.
Funny thing too, I had myself convinced that the added weight of a bow quiver was a good thing for my longbow but when I took the bow quiver off, my long bow felt SOOOOO much better to shoot. It's been gathering dust ever since.
The side stalker came with a "one arrow" bow quiver thing that is just a sheath for a broadhead that ties to the upper limb and you insert the broadhead there and hold the shaft in your hand along with the bow handle. It's right there till you need it and is real handy.