The relative performance of local kernel estimators over global estimators of smooth distribution functions is investigated in this paper. This is achieved by obtaining expressions for the relative efficiency and the asymptotic relative efficiency of kernel estimators of distribution functions. Relative efficiencies and asymptotic relative efficiencies are computed for some characteristic distribution for finite random samples. The resulting relative performance and asymptotic relative efficiency to asymptotic relative efficiency is also noted. A comparison of relative efficiencies given different kernels is also investigated.