Understanding the physics of multiphase plumes and their simulation through numerical modeling has been an important area of research in recent times in the area of environmental fluid mechanics. The two renowned numerical modeling types that are commonly used by researchers today to simulate multiphase plumes in nature are the mixed-fluid and the two-fluid integral models. In the present study, a detailed review was performed to study and analyze the two modeling approaches for the case of a double plume (upward moving inner plume with downward moving annular outer plume) with the objective of ascertaining which of these models represent the prototype physics in the integral plume model equations with a higher degree of completeness and accuracy. A graphical user interface was designed to facilitate running the models. By comparison to laboratory scale experimental data and through sensitivity analyses, a rigorous effort was made to determine the most appropriate choice of initial conditions needed at the start of the model computation and at the peeling locations and to obtain the most consistent values of the different model parameters that are necessary for calibration of the two models. Consequently, with these selected sets of initial conditions and model parameters, the models were run and their outputs compared against each other for three different case studies with ambient conditions typical of real environmental data. The dispersed phases considered were air bubbles in two cases and liquid CO2 droplets for the third case, with water as the continuous phase in all cases. The entrainment coefficient was found to be the most important parameter that affected the model results. In all the three case studies conducted, the mixed-fluid model was found to predict about 30% higher values for the peel heights and the DMPR (Depth of Maximum Plume Rise) than the two-fluid model.