We consider the issue of wave-breaking closure for the well known Green-Naghdi model and attempt at providing some more understanding of the sensitivity of some closure approaches to the numerical setup. More precisely and based on we used two closure strategies for modelling wave-breaking of a solitary wave over a slope. The first one is the hybrid method consisting of suppressing the dispersive terms in a breaking region and the second one is an eddy viscosity approach based on the solution of a turbulent kinetic energy model. The two closures use the same conditions for the triggering of the breaking mechanisms. Both the triggering conditions and the breaking models themselves use case depended / ad/hoc parameters which are affecting the numerical solution wile changing. The scope of this work is to make use of sensitivity indices computed by means of Analysis of Variance (ANOVA) to provide the sensitivity of wave breaking simulation to the variation of parameters such as the mesh size and the breaking parameters specific to each breaking model. The sensitivity analysis is performed using the UQlab framework for Uncertainty Quantification.