This work compares the performance of two Lagrangian turbulent particle dispersion models: the standard model (e.g., that presented in Sommerfeld et al. (1993)), in which the fluctuating fluid velocity experienced by the particle is composed of two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, and the model proposed by Minier and Peirano (2001), which is based on the PDF approach and performs closure at the level of acceleration of the fluid experienced by the particle. Formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping the mathematical manipulation of the stochastic model simple, thereby avoiding some pitfalls and simplifying the derivation of macroscopic relations. The performance of both dispersion models is tested in the configurations of grid-generated turbulence (Wells and Stock (1983) experiments), simple shear flow (Hyland et al., 1999) and confined axisymmetric jet flow laden with solids (Hishida and Maeda (1987) experiments).