There really isn't a whole lot of difference between Hill, Switch and River cane other than height, slight variations in density and growing locations. At least that is what I read and supposedly they all make good arrows. Their scientific names are Hill Cane - Arundinaria appalachiana, River or Giant Cane - Arundinaria gigantea, and Switch Cane - Arundinaria tecta. So as you can see, they are all different forms of Arundinaria. I looked up up on the USDA website. It tells you a lot of information like growing locations and stuff. Here is the link if you have not already visited their website. http://plants.usda.gov/java/nameSearch I use it for finding out what native material is growing in my area.
You are pretty lucky that you have some of that stuff growing wild in your area. I would love it if that stuff grew naturally here in Pennsylvania. So far, I am making due with Multiflora Rose and Amur Honeysuckle! I have some cut and I am waiting impatiently for it to dry!