In this work we focus on the binding of excess electrons to water clusters, a problem for which dispersion interactions, which originate from long-range correlation effects, are especially important. Two different model potential approaches, one using quantum Drude oscillators and the other using polarization potentials, are investigated for describing the long-range correlation effects between the weakly bound excess electron and the more tightly bound electrons of the monomers. We show that these two approaches are related in that the polarization potential models can be derived from the quantum Drude model approach by use of an adiabatic separation between the excess electron and the Drude oscillators. The model potential approaches are applied to clusters containing up to 45 water monomers. Where possible, comparison is made with the results of ab initio electronic structure calculations. Overall, the polarization potential approach is found to give electron binding energies in good agreement with those from the Drude model and ab initio calculations, with the greatest discrepancies being found for "cavity-bound" anion states.