Particle laden flows are often modeled using one of two numerical approaches: Euler-Lagrange and Euler-Euler. The Euler-Lagrange approach analyzes the particulate phase from a control mass perspective, then the solid particulate phase is coupled to a (continuous) fluid phase based on the underlying fluid-flow equations formulated within an Eulerian model. The Euler-Euler approach, however, applies the Eulerian formulation for both the fluid and particulate phase. The aim in this effort is to evaluate the approaches in the context of a two-dimensional, compressible gas flow laden with particulate and impinging on a normal surface. Such flows are relevant to classes of solid rockets, sandblast nozzles, and other particle-laden flows in the context of converging-diverging nozzles. Several comparisons are made between both approaches. This first pertains to model accuracy of the particulate flow, which involves comparing particle velocities and distributions throughout the numerical domain. In addition, the computational time required to solve particle flow in a compressible gas flow was compared between both numerical approaches. The Euler-Euler approach presented a lower computational time to solve particle flow for the rocket jet compared to the Euler-Lagrange approach. The Euler-Euler approach also showed a lower computational cost than that of the Euler-Lagrange approach to reach a steady solution. Also, a numerical validation of an under-expanded jet case was performed using the Euler-Euler approach. The results of the simulation agreed strongly with experimental measurements.