Mesoscale eddies are the strongest currents in the world oceans and transport properties such as heat, dissolved nutrients, and carbon. The current inability to effectively diagnose and parameterize mesoscale eddy processes in oceanic turbulence is a critical limitation upon the ability to accurately model large-scale oceanic circulations. This investigation analyzes the Lagrangian statistics for four faster and less computationally expensive eddy-permitting models---Biharmonic, Leith, Jansen & Held Deterministic, and Jansen & Held Stochastic---and compares them against each other and an eddy-resolving quasigeostrophic Reference model. Results from single-particle climatology show that all models exhibit similar behavior in large-scale movement over long times scales and their Lagrangian statistics display Gaussian behavior. However, differences between the models arise in smaller-scale particle-pair climatology. Root-mean-square forecasting errors are found to be uniform across models because the error in the initial condition affects the accuracy of the forecast more than the model chosen.