Discrete particle simulation has been recognized as a useful numerical technique for elucidating the fundamentals of granular matter. For gas-solid two-phase now in fluidization, such simulations are achieved by combining the discrete flow of the particle phase with the continuum flow of the gas phase. However, differences exist in the actual implementation of this idea in the literature. This paper attempts to rationalize this matter by discussing important aspects including the governing equations in relation to the so-called models A and B, which use different treatments of pressure drop in the well-established two-fluid model, different coupling schemes between the gas and solid phases, and different equations for quantifying the particle-fluid interaction. For the purpose of quantitative analysis, gas fluidization of binary mixtures of particles is simulated with different model formulations, and a comparison of the results in terms of flow pattern and mixing/segregation kinetics shows a significant difference. Physical experiments are then conducted under similar conditions to assess the two model formulations, and the results suggest that the model B treatment is favored. The reason for the difference is also discussed in terms of the particle-fluid interaction force. On this basis, a method to reduce the difference between the two model formulations is proposed and tested.