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In this paper, the importance of model horizontal resolution in mixing and dispersion is investigated by comparing two data‐assimilative high‐resolution simulations (4 and 1 km), one of which is submesoscale‐permitting. By employing both Eulerian and Lagrangian metrics, upper‐ocean differences between the mesoscale‐resolving and submesoscale‐permitting simulations are examined in the northeastern Gulf of Mexico, a region of high mesoscale and submesoscale activity. Mixing in both simulations is explored by conducting Lagrangian experiments to track the generation of Lagrangian coherent structures (LCSs) and their associated transport barriers. Finite‐time Lyapunov exponent (FTLE) fields show higher separation rates of fluid particles in the submesoscale‐permitting case, which indicate more vigorous mixing with differences being more pronounced in the shelf regions (depths ≤ 500 m). The extent of the mixing homogeneity is examined using probability density functions (PDFs) of FTLEs with results suggesting that mixing is heterogeneous in both simulations, but some homogeneity is exhibited in the submesoscale‐permitting case. The FTLE fields also indicate that chaotic advection dominates turbulent mixing in both simulations regardless of the horizontal resolution. In the submesoscale‐permitting 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. Plain Language Summary: Small‐scale processes (0.1–50 km) play a critical role in upper‐ocean water transport and mixing. Thus, the added value from resolving these finer scales in numerical models is evaluated by comparing two high‐resolution numerical simulations in the northeastern Gulf of Mexico: one at 1 km horizontal resolution that truly resolves features on the order of 10 km and one at 4 km that only resolves features greater than 50 km. Passive fluid particle experiments are conducted to document the mixing and identify structures that act as barriers to transport between fluids with different properties and determine the fate of dispersants in the ocean. In both simulations, the particles' distribution is spatially heterogeneous, which indicates that mixing is largely controlled by these structures. Results also show that neighboring fluid particles separate faster from one another in the 1 km simulation than in the 4 km simulation, meaning that mixing of fluids is more intense. Lastly, we find that the 1 km simulation is more realistic when applied to oil particle dispersion at the location of the Deepwater Horizon oil spill. Key Points: Resolving submesoscale motions leads to increased Lagrangian transport and mixing as well as the generation of more intricate LCSsChaotic advection dominates turbulent mixing regardless of the horizontal model resolution (either 4 km or 1 km)Submesoscale‐permitting simulation yields reduced error against drifter observations compared to mesoscale‐resolving counterpart [ABSTRACT FROM AUTHOR]