Both of the boundary conditions are used to simulate large periodic structures such as a phase array or high impedance surfaces. The difference is that in case of PBC, a phase shift at the boundary(ies) can be specified. This can be accessed in the "Phase Shift/Scan Angle" tab in the same dialogue box after choosing PBC at one or more axes. The PBC may, therefore, be more helpful when studying near-field problems (as suggested in CST help page) like a single element of a phased array. The phase-shift fields are not editable when the unit cell boundary is chosen. Only scan angles are required for simulation in unit cell boundary condition.
I have used prior Unit Cell boundary conditions to characterize unit cell of a high impedance surface, where a single unit cell is replicated in XY plane. While the principle remains the same in PBC's, I hope someone can clarify more as I haven't used them until now.