Theory: Pinhole camera with no DOF shoots all rays from single point. Camera with DOF shoots ray randomly originating from a shape of the aperture (circle, n-gon, custom image). Only the ray origin moves, ray direction is constructed so that all rays for single pixel created from all positions on the aperture intersect in a single point in the focal distance.
Comparison: Rendered DOF is the correct solution with MUCH better quality. Post-pro DOF is fake with inferior results - but much faster, with the option to re-focus, so it is a tradeoff. Rendered DOF is better quality, postpro DOF is faster, siple. Deep data/OpenEXR 2.0 helps, but probably does not solve the problem completely.