We investigate the ability of uncertainty quantification techniques to act as enablers for the study of the sensitivity of dynamics of dam breaks to the variations of model parameters. In particular, we make use of sensitivity indexes computed by means of an Analysis of Variance (ANOVA) to provide the sensitivity of the runup dynamics to the variations of parameters such wave amplitude, friction coefficient, etc. The sensitivity indexes, known as Sobol indexes, are obtained following (Crestaux-LeMaitre-Martinez, 2009) by resorting to a non-intrusive polynomial chaos method allowing to reconstruct a complete representation of the variation of the outputs in the parameter space, and to compute the sensitivity indexes via the ANOVA decomposition. To increase the reliability of the results, we perfom the study independently with two models based on a discretization of the shallow water equations, developed in (Ricchiuto, 2014), and (Nikolos and Delis, 2009), respectively. The approach proposed provides simultaneously the variance of the outputs and their sensitivity to each independent parameter, allowing to construct a hierarchy of parameters which depends on the flow conditions.