For climate change impact studies, bias correction methods are widely utilized to improve climate model outputs by correcting the representation of climate variables. In addition to the univariate bias correction methods, many multivariate bias correction methods have been proposed, using diverse mathematical concepts in their individual designs. Although several attempts have been made to evaluate the performance of the multivariate bias correction methods, there is no exploration in the impact of diverse configurations to target multivariate dependencies in the multivariate bias correction methods particularly for hydrological modeling. This study tackles this research gap by developing an inter-comparison framework that assesses how the different configurations affect the climate and hydrological simulations. To achieve the research goal, the impact of three configurations (inter-variable, inter-spatial, and full-dimensional dependence configurations) is evaluated on multiple basins in a national-scale domain over South Korea. Results show that although most methods in the three different configurations capably correct the statistics, some instabilities are also observed when a high-dimensional dependence configuration is used, informing that some multivariate bias correction methods may not be compatible with high-dimensional configurations. For hydrological modeling, the configuration definitions bring about distinct differences in streamflow realizations. Only some of the inter-variable and full-dimensional configurations perform better or similarly to univariate bias correction methods. Finally, we demonstrate the importance of selecting bias correction methods while addressing the necessity for further improvement.