Cable-Driven Parallel Robots (CDPRs) constitute a class of robots which displace a load by means of cables. In particular, the use of cables to guide the end-effector continues to be a challenging task. Indeed, several Tension Distribution Algorithms (TDAs) have been developed so far to properly steer the load. Although comparisons between them have been made, no performance index is established to evaluate numerically such methods. Therefore, this paper aims at defining a performance index establishing the sensitivity of a TDA by looking at the maximum tension variation that stems from a change in the external wrench. This would help both comparing and choosing the proper TDA among the existing ones. The definition of the index pops out naturally from the linearization of the equations defining the optimization problems. Commonly used TDAs are compared using the defined index. In order to show an application of it, a planar CDPR is considered and its Wrench-Feasible Workspace (WFW) is characterized by the index defined.