Some days I shoot better with the quiver on, some days with it off, so I don't think (for me) it's that much of a factor in shooting. I does make the bow quieter, which is a real plus for hunting IMHO.
It also is the handiest place I have found to keep extra arrows. With side or back quivers, I am constantly snagging them on brush or weeds. They are also more of a pain to get arrows from quiver to bow, for me at least. Also, if I'm turkey hunting, I don't need anything else hanging on me. I already have my pack, my decoy bag, and my blind slung over my shoulders. There is no more room! So carrying the arrows in a bow quiver is the best answer.
As far as bow quivers go, I have used Selway, Boa, Eagle Flight, and currently a Thunderhorn Linx. The Linx is the heaviest because it has an aluminum bar that keeps the hood and arrow clip from sliding apart. The bar is also the reason this is my favorite quiver so far. You put it on with Boa-type straps and it stays right there until you are ready to take it off...no shifting at all!
There, you got more information and opinion than you asked for. :rolleyes: