In this study, a framework to circumvent the difficulties in selecting a proper flood routing method was established by employing two different multi-criteria decision analysis (MCDA) tools, namely, TOPSIS and PROMETHEE, with definite decisive criteria such as the error metrics, the number of model parameters, and the model background, under three scenarios. For eight distinct flood datasets, the parameters of 10 different Muskingum models were determined using the water cycle optimization algorithm (WCOA) and the performance of each model was ranked by both MCDA tools considering the hydrograph types of flood datasets, labeled as smooth single peak, non-smooth single peak, multi-peak, and irregular. The results indicate that both tools were compatible by giving similar model results in the rankings of almost all scenarios that include different weights in the criteria. The ranking results from both tools also showed that the routing application in single-peak hydrographs was examined better with empirical models that have a high number of parameters; however, complex hydrographs that have more than one peak with irregular limps can be assessed better using the physical-based routing model that has fewer parameters. The proposed approach serves as an extensive analysis in finding a good agreement between measured and routed hydrographs for flood modelers about the estimation capabilities of commonly used Muskingum models considering the importance of correlation, model complexity, and hydrograph characteristics.