The increasing realism of ocean circulation models is leading to an increasing use of Eulerian models as a basis to compute transport properties and to predict the fate of Lagrangian quantities. There exists, however, a significant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles. These scales may contain high vorticity coherent structures that are not resolved due to computational issues and/or missing dynamics and are typically suppressed by smoothing operators. In this study, the impact of smoothing of the Eulerian fields on the predictability of Lagrangian particles is first investigated by conducting twin experiments that involve release of clusters of synthetic Lagrangian particles into "true" (unmodified) and "model" (smoothed) Eulerian fields, which are generated by a QG model with a flow field consisting of many turbulent coherent structures. The Lagrangian errors induced by Eulerian smoothing errors are quantified by using two metrics, the difference between the centers of mass (CM) of particle clusters, ρ, and the difference between scattering of particles around the center of mass, s. The results show that the smoothing has a strong effect on the CM behavior, while the scatter around it is only partially affected. The QG results are then compared to results obtained from a multi-particle Lagrangian Stochastic Model (LSM) which parameterizes turbulent flow using main flow characteristics such as mean flow, velocity variance and Lagrangian time scale. In addition to numerical results, theoretical results based on the LSM are also considered, providing asymptotics of ρ, s and predictability time. It is shown that both numerical and theoretical LSM results for the center of mass error (ρ) provide a good qualitative description, and a quantitatively satisfactory estimate of results from QG experiments. The scatter error (s) results, on the other hand, are only qualitatively reproduced by the LSM.