We present a comparison of the quantitative information obtained about the energetic heterogeneity of silica-supported nickel catalysts by an analysis of an experimental TPD peak using the absolute rate theory, in the form of the Wigner-Polanyi equation, and the statistical rate theory of interfacial transport. A new method of evaluating the desorption energy distribution, based on an improved condensation approximation approach and applicable to thermodesorption kinetics in both the above approaches, has been developed for this purpose. To make the comparison, a literature report of a study of adsorption equilibria in the hydrogen/SiO2-Ni system is used together with a TPD study of our own sample of the catalyst. The use of the Wigner-Polanyi approach resulted in the recovery of energy distribution functions showing the solid surface to be more energetically heterogeneous than it is when one uses the SRTIT approach on the same data. The broader surface energetic heterogeneity calculated using the Wigner-Polanyi approach is especially dramatic in the systems where significant readsorption occurs. This is because readsorption affects TPD peaks in a similar way to that due to surface heterogeneity. Despite this, the Wigner-Polanyi approach is commonly applied, neglecting the readsorption term, because of fundamental problems connected with using the full ART formulation, with the readsorption term included. We find that in general, for the same set of physical parameters characterizing a given gas/solid adsorption system, the Wigner-Polanyi approach will generate theoretical TPD peaks which are narrower, and shifted toward lower temperatures, compared with matching theoretical TPD peaks generated by the SRTIT approach, Clearly, one of these approaches is misleading, and on the basis of various considerations presented below, arguments are put forward favoring the use of the SRTIT approach for the interpretation of TPD peaks.