The purpose of the paper is to compare two successful families of stochastic model for the prediction of inertial particles dispersion in a turbulent channel flow. Both models are based on the Langevin equation; nevertheless, they were developed following different paths. The first model considered is named "Drift Correction model (DCM)", and the second one is the "Generalized Langevin Model (GLM)". To examine the capabilities of both models, a comparison of the results predicted by the DCM- and GLM-type dispersion models with those extracted from a Direct Numerical Simulation (DNS) is conducted. In the limit of vanishing particle inertia, both models can accurately predict second-order statistics. It is also noticed, as not expected, that they are very similar when they are written in the same functional form. The comparison has also been conducted with DNS data of a particle-laden channel flow. The comparison of particle statistics (such as concentration, mean and rms particle velocity, third-order particle velocity correlations) shows that both stochastic models give very satisfactory results up to second-order statistics. The DCM- and GLM-type dispersion models studied can capture the main physical mechanisms that govern particle-laden turbulent channel flows. (C) 2016 Elsevier Ltd. All rights reserved.