The ability to predict critical lines of members of the methane-, perfluoromethane- and water-alkanes homologous series is compared for van der Waals (vdW)-type and Carnahan-Starling (CS)-type equations of state, A temperature dependent combining rule for the binary attraction parameter is discussed and employed. It is found that the appropriate choice of the adjustable parameters yields quite accurate results for both equations. A new application of global phase diagrams is proposed for the quantitative description of real mixtures. In this diagram, the boundaries of the different types of phase behavior are presented in the k(12)-l(12) plane. Analysis of this diagram has allowed us to reach conclusions that cannot be obtained by a simple fit of data points. In particular, it is demonstrated that the global phase diagram's shape defines the correlative ability of the equations. It is found that CS-type equations tend to predict a larger region of liquid-liquid immiscibility, the accuracy of the result depends on the particular experimental system. Changes in the density dependence of the attraction term of the two-parameter equations influence mostly the predicted critical volumes and not their qualitative performance. In addition, the development of a CS-type equation suitable for engineering calculations is discussed.