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@Bill, with identical framing the dof does differ. Obviously a 50 is still a 50 but because it acts like an 80 you stand farther away the end result is a deeper dof for a crop sensor. Equivalence is the key word

The key to understanding, from an engineering perspective, is to hold everything except one constant, and by changing that one variable, see what the difference is.  If you change sensors, and also move the sensor further from your subject, you are changing two things, or more, at the same time.   I appreciate that you might want the same framing, so will use the camera this way.  I also appreciate that you can get that much closer to your subject for a portrait if you use a full frame body and the same lens.  I agree with Bill though.  The sensor size does not affect DOF.  How you decide to use it might, but that is the usage, not physics.  If we skip portraits for a moment and look at macro, the lens will be in the same place for both sensors, and the full frame sensor will just record more space around my subject.  DOF will be identical with both sensors because focal length, aperture and distance will be constant.  The same can be said if you are using a telephoto lens to take something far away, because you cannot get closer — standing on shore and shooting a boat that is sailing for instance.