Peptide recognition domains (PRDs) are ubiquitous protein domains which mediate large numbers of protein interactions in the cell. How these PRDs are able to recognize peptide sequences in a rapid and specific manner is incompletely understood. We explore the peptide binding process of PDZ domains, a large PRD family, from an equilibrium perspective using an all-atom Monte Carlo (MC) approach. Our focus is two different PDZ domains representing two major PDZ classes, I and II. For both domains, a binding free energy surface with a strong bias toward the native bound state is found. Moreover, both domains exhibit a binding process in which the peptides are mostly either bound at the PDZ binding pocket or else interact little with the domain surface. Consistent with this, various binding observables show a temperature dependence well described by a simple two-state model. We also find important differences in the details between the two domains. While both domains exhibit well-defined binding free energy barriers, the class I barrier is significantly weaker than the one for class II. To probe this issue further, we apply our method to a PDZ domain with dual specificity for class I and II peptides, and find an analogous difference in their binding free energy barriers. Lastly, we perform a large number of fixed-temperature MC kinetics trajectories under binding conditions. These trajectories reveal significantly slower binding dynamics for the class II domain relative to class I. Our combined results are consistent with a binding mechanism in which the peptide C terminal residue binds in an initial, rate-limiting step.