In this paper, the importance of model horizontal resolution in identifying the nature of mixing and dispersion is investigated by comparing two data-assimilative, high-resolution simulations (4km and 1km), one of which is submesoscale-resolving. By employing both Eulerian and Lagrangian metrics, upper-ocean differences between the mesoscale- and submesoscale-resolving simulations are examined in the northeastern Gulf of Mexico, a region of high mesoscale and submesoscale activity. The nature of mixing in both simulations is identified by conducting Lagrangian experiments to track the generation of Lagrangian Coherent Structures (LCSs) and their associated transport barriers. Finite-time Lyapunov exponents (FTLE) fields show higher separation rates of fluid particles in the submesoscale-resolving case which indicate more vigorous mixing, with differences being more pronounced in the shelf regions (depths<=500m). The extent of the mixing homogeneity is examined by using probability density functions (PDFs) with results suggesting that mixing is heterogeneous in both simulations, but some homogeneity is exhibited in the submesoscale-resolving case. The FTLE fields also indicate that chaotic stirring dominates turbulent mixing in both simulations regardless of the horizontal resolution. In the submesoscale-resolving experiment, however, smaller scale LCSs emerge as noise-like filaments that suggest a larger turbulent mixing component than in the mesoscale-resolving experiment. The impact of resolution is then explored by investigating the spread of oil particles at the location of the Deepwater Horizon oil spill.