when I'm hunting in a stand, which is mostly what I do; I always take my quiver off the bow. I find it easier to manuver and shoot so I use a one piece quiver. When I take the quiver off there is no noise to worry about. If you are planning on hunting the ground or any stalk type hunting in open terrain then the two piece might be your best bet since it is firmly attatched to the bow. As for the noise, I couldn't say if it would be any quieter than a one piece quiver and there is no evidence that I know of to say yes or no.
TightSpot Quiver I gotta tell ya -- Tightspot Quiver not only assist with your stabilization of your bow but its so lightweight and durable that it is almost unnoticeable. It may cost alittle more but in the long run its worth it..Also, the ergonmics of the quiver holds extremely tight to your bow eliminating the need to remove it..
It may if your one piece is a POS. If it's a quality one piece then I doubt it will make a difference. My Treelimb Premium is as quiet as any quiver I've ever shot and I used to be a real diehard 2 piece guy for the noise issue.
I prefer a two piece quiver mainly because I like having the arrows right at my fingertips and also because two piece quivers will (for the most part) sit closer to the bow and thus won't mess with the balance of the bow so much. Just my .02 (I also agree with Kodiak, a good quality one piece quiver is the only way to go if you choose that route)