I automatically default to a bow quiver for 95% of my hunts. The hip quiver is my go-to for certain unique situations. I've strapped a loaded hip quiver to my pack when needed, but obviously not while actively hunting. I've used a hip quiver on a horseback hunt and it worked great. I would never use one for treestand hunting, nor would I likely want it if hiking/hunting longer distances.
Pro for the bow quiver is the obvious immediate access to your arrows. Secondary pro might be the additional mass weight which can be a bit of a stabilizer if you will.
Con for the bow quiver (for me) is the fact that wherever the bow goes...meaning carrying through the brush, swinging into position at the moment of truth, etc....the arrows go with it. That can mean additional noise or arrow wear. My fletch take a bit of abuse on a longer backcountry hunt. Also, many times a bowhunter on the ground is shooting from behind or near some form of cover, be it a rock outcrop, tree, clump of brush or a blind of some sort. Arrows in a bow quiver can easily make unwanted contact with whatever is hiding the hunter, especially when the bow arm is extended to make the shot. In very tight settings, a bow quiver can be an outright liability.