MM/PBSA is simply a post-processing technique whereby the free energy of a state is calculated from the internal energy (MM) of the molecule and its interaction with an implicit representation of solvent (PBSA). FEP, like other free energy evaluations (TI, BAR, etc) evaluates free energy differences of a given configuration under a different Hamiltonian (i.e. one whose interactions are scaled by a lambda factor). Calculations that make use of FEP are much more expensive than MM/PBSA, which uses a single trajectory, run using normal MD.
While other free energy methods, like TI and BAR, are more accurate than MM/PBSA, they are prohibitively expensive for larger solutes like macromolecules. For evaluating binding free energies where the ligand to be decoupled is small, most people opt for the more accurate methods. For solvation free energies of proteins, DNA, etc, MM/PBSA is sufficiently accurate and avoids the huge expense that would arise from using decoupling methods.