To better understand the comment above you need to understand stiffness. When you take a wire of steel, which is very strong, you'll find you can actually bend

To better understand the comment above you need to understand stiffness. When you take a wire of steel, which is very strong, you'll find you can actually bend it very easily. If this kind of stress is what the material will face, you could replace the wire by a thin tube which will be much more rigid -- you probably don't want your structure bending and deforming. In this case, where stiffness is more important, it's more important that the material is light so you can make it larger yet proportionally stiffer per unit weight by using an adequate structure -- e.g. a tube or large diameter (this is because the bending stiffness increases more-than-linearly with diameter). Now suppose instead you were trying to traction the wire (pull it). There's no structural change that will make it stiffer -- in this case all you may want is that it is very strong -- in which case you simply go for the best strength/weight or just pure strength.