Wool excels in damp conditions but it's not a miracle fabric. It does absorb some sweat odor after a while, just not nearly as bad or as soon as synthetics do. You might not smell your own stink on it, but other people can. I know this because wool used to be THE only fabric for cycling jerseys and shorts, and apparently some guys thought they never had to wash them.
When wet, it smells a little like wet dog fur, so if that bothers you, steer clear.
Like cotton, it is somewhat flame-resistant so it doesn't automatically melt holes if you get an ash or hot utensil on it--unlike synthetics.
The biggest drawback to wool is that moths eat it. Heartbreaking to find their holes in heirloom wool blankets or expensive clothing. So store it with that in mind.
It can last a long time if well-made and properly cared for. In my experience, NikWax Wool Wash is the best "soap" for wool. It is hard to find around the Denver area, though.