In a paper by Abrahamson , it is shown that the Kuiper test generally performs better than the Kolmogorov-Smirnov (K-S) test according to exact Bahadur relative efficiency. The present note concerns the Bahadur efficiency of a related test statistic $U_n$ whose exact null probability distribution is available in the two-sample case with equal sample sizes. It is shown that $U_n$ is often more efficient than the K-S test and may even be as efficient as the Kuiper test.
"On the Efficiency of a Competitor of the Two-Sample Kolmogorov-Smirnov and Kuiper Tests." Ann. Math. Statist. 43 (6) 1991 - 1992, December, 1972. https://doi.org/10.1214/aoms/1177690871