Down is good for insulation while mountaineering, winter camping, ice fishing and other activities where you'll be exposed to very cold, dry conditions. Once it's wet, you will never dry it in the field. It is very durable, if high quality, and highly compressible. I have two down parkas and a sleeping bag. My wife has a down parka and down expedition mitts.
Wool is good for insulation when you are hunting, snowshoeing (in layered applications only!), and any other time when moisture can be an issue. My wife once fell into a lake at a canoe launch wearing an Icelandic wool sweater. She popped back up and discovered that everything under the sweater stayed dry during the immersion.
Cotton is what you wear back at the lodge while telling lies about the shot you passed on earlier that day.