© 2016 The International Society of Offshore and Polar Engineers. Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) are well known computational fluid dynamics (CFD) methods that are used to solve fluid dynamics problems in a meshfree Lagrangian framework. Both the SPH and MPS are well suited for simulating large deformation and the fragmentation of the free surface. They use a particle system for numerical simulation; however, there are some differences in numerical schemes and equations including differentiation, pressure calculation, and treatment of boundary conditions. The classical test cases of the particle method, two-dimensional broken dam, and harmonically oscillated sloshing tank are selected for a comparative study. The standard weakly compressible (WC) SPH parallel solver, DualSPHysics, and the in-house Moving Particle Semi-implicit solver are used in this study. For a quantitative comparison of respective viscous parameters, the broken dam problem is studied through the use of free surface snapshots. Those two numerical methods are also compared with corresponding experiments. In the case of the harmonically oscillated sloshing tank, the free-decay natural periods, sloshing impact pressure, and free surface profile are compared with the corresponding measurements. Through the comparative study, several minor differences are observed. The MPS is typically computationally more intensive in dealing with a large number of particles due to the pressure Poisson equation. In contrast, the SPH is computationally efficient, but the pressure fluctuation can be problematic when a sufficiently large number of particles are not used. Also, in the SPH, the unphysical gap between fluid particles and wall particles is observed. The relative merits of the two particle methods for solving free surface academic problems are discussed.