The Wilkinson stick is a great performer. As you pointed out it has a unique formula. It is one of my favorite sticks for sure.Wilkinson sticks are very good. They use a tallow-based soap with lanolin and glycerin added. Imagine a stick that is like a cross between Tabac and Mitchell's Wool Fat, but smells like marine bath soap from a hotel, with an electric blue color.
Note: the stick is a completely different soap from the Wilkinson blue tub. The tub is not very good.