The study of the structure and chemistry of biological systems with density-functional theory requires an accurate description of intermolecular interactions involving charged moieties. While dispersion-corrected functionals accurately model noncovalent interactions in neutral systems, a systematic study of the performance and errors associated with intermolecular interactions between charged fragments is missing. We undertake this study by examining the performance of a series of dispersion-corrected functionals with varying degrees of exact exchange for the side-chain protein interactions from the BioFragment Database (BFDb) of Burns et al. (the SSI set). In general, hybrid functionals with 20-30% exact exchange are accurate across the board, with the lowest mean absolute errors of 0.11 kcal/mol obtained from the 20% exact-exchange BLYP and PW86PBE hybrids coupled with the exchange-hole dipole moment (XDM) dispersion model. In addition, our analysis shows that functionals with higher exact-exchange fractions overestimate the electrostatic contributions to the binding energies, and that GGA functionals overestimate zwitterion binding energies due to delocalization error and overestimated charge transfer. In addition, the (quite large) repulsion in the dications is systematically overestimated by all functionals, and the trends for the monoanionic and dianionic dimers can be successfully explained by appealing to the ability of the underlying GGA to describe Pauli repulsion, as given by its exchange enhancement factor. Going beyond studies of biomolecules, this latter result has important implications for selecting appropriate GGA functionals for applications to ionic solids and layered materials containing anion-anion interactions.