Lagrangian numerical methods are particularly suitable to reproduce flows involving large and rapid deformation of the domain, fluid splitting and coalescence, jets and sprays. The absence of the convective terms in the governing equations avoids numerical diffusion. This paper provides a comparative study between two Lagrangian particle models based on the Smoothed Particle Hydrodynamics (SPH) and the Particle Finite Element Method (PFEM). The description of the methods is provided; features and drawbacks of each method are compared and discussed. The introduced models, which represent widely used advanced analysis tools, are compared and validated in the simulation of five test cases: Two solitary waves, two regular wave trains and a non-linear wave-structure impact. Results from each model are similar and quite close to reference data. Therefore, both models have been validated against new test cases never simulated before, showing that these models can be effectively used for the analysis of regular and non-linear wave with structure impact.