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The objective of this study is to assess the impact of a dense-phasetreatment on the hydrodynamic description of granular, binary mixtures relativeto a previous dilute-phase treatment. Two theories were considered for thispurpose. The first, proposed by Garz\'o and Dufty (GD) [Phys. Fluids {\bf 14},146 (2002)], is based on the Boltzmann equation which does not incorporatefinite-volume effects, thereby limiting its use to dilute flows. The second,proposed by Garz\'o, Hrenya and Dufty (GHD) [Phys. Rev. E {\bf 76}, 31303 and031304 (2007)], is derived from the Enskog equation which does account forfinite-volume effects; accordingly this theory can be applied to moderatelydense systems as well. To demonstrate the significance of the dense-phasetreatment relative to its dilute counterpart, the ratio of dense (GHD) todilute (GD) predictions of all relevant transport coefficients and equations ofstate are plotted over a range of physical parameters (volume fraction,coefficients of restitution, material density ratio, diameter ratio, andmixture composition). These plots reveal the deviation between the twotreatments, which can become quite large ($>$100%) even at moderate values ofthe physical parameters. Such information will be useful when choosing whichtheory is most applicable to a given situation, since the dilute theory offersrelative simplicity and the dense theory offers improved accuracy. It is alsoimportant to note that several corrections to original GHD expressions arepresented here in the form of a complete, self-contained set of relevantequations.

Enskog Theory for Polydisperse Granular Mixtures. III. Comparison of  dense and dilute transport coefficients and equations of state for a binary  mixture