I'm new to flooring too, but wool is the only non-synthetic carpet (Although sorona by dupont is sometimes considered a mix of natural and synthetic). Wool is the best for retention. So in other words, after ten years of use, it will look closer to what it looked like when it was installed, than a synthetic carpet. Also it has better resistance to fire, so it is a very good idea to install carpet near fire, if they need carpet there.
Wool as a fibre has a natural spring to it, so it's harder to leave footprints and vacuum marks. Also I think it doesn't have problems with static, but I may have that wrong. The downside is cost and soiling. Also, as a side note, wool shouldn't affect people with asthma as the shedding (another problem with wool) is too big to breathe in. Hope that helped.