In this paper, we compare the strength of alternate formulations (polyhedra) of the binary knapsack set. We introduce a specific class of knapsack sets for which we prove that the polyhedra based on their minimal cover inequalities (together with the bounds on the variables) are strictly contained inside the polyhedra defined by their continuous knapsack relaxations. Furthermore, we answer an open question in the literature by establishing that for the knapsack sets belonging to this class, the formulations based on minimal covers provide their complete convex hull. Finally, we prove that the convex hull of a knapsack set violating some of the conditions required to define the above specific class can never be completely described just by its minimal cover inequalities.