Likewise, on it's own, while tungsten may have a high strength under tension (tensile strength), it is usually extremely brittle, and dense - so objects made out of it are heavy for their size - not so hot for armor and weapons. In pure form, it has the highest melting point of any metal, iirc.
The usually most useful form of tungsten is in tungsten carbide (half tungsten, half carbon) - the stuff is hard (in the mineralogical sense - it is very scratch resistant), and has a high melting point, making it good for cutting surfaces of high-speed cutting tools and drills. Swords and arrows, though, don't need that kind of protection most of the time.
It is hard or impossible to rate fantasy metals against real ones, because we are never given good comparisons in the fiction.