Two different computation methods were used to calculate the binary interaction parameters of both the Soave-Redlich-Kwong and the Peng-Robinson equations of state with the quadratic van der Waals’ mixing rules. Experimental vapor-liquid equilibrium data, for nine binary systems, were selected in four different classes of polar and non-polar compounds. These test systems consist of four CO2-containing mixtures, two asymmetric mixtures, and one binary of each of methane, hydrogen-containing, and symmetric mixtures. The experimental data cover a wide range of temperature and pressure. In the first computation method, the non-linear least squares, based on a modification of the Levenberg-Marquardt minimization algorithm, was used to minimize the sum of the squares of residuals of the natural logarithm of equilibrium ratios. The second computation method is based on the maximum likelihood method, where both independent and dependent variables are subject to error. The objective function applied in this computation method, the sum of the squares of residuals of the measured variables divided by the statistical variances associated with these variables, was minimized subject to the phase equilibrium constraints including the minimum Gibbs free energy. The same routine for density calculations was used in both computation methods. The results of this comparative study revealed that the second computation method is more superior for both equations of state. The results also demonstrate that different computation techniques can result in different conclusions using the same equation of state for the same equilibrium systems. This conclusion suggests that the shortcomings in different equations of state stem not only from the equations themselves but also from the computational methods applied.