I'm going back to the original post, and I will eschew all the scenario variations.
n1as wrote in post #15595460
To get the same field of view, the crop-sensor camera needs to shoot with a shorter lens. The shorter lens yield wider DOF. Is that why the crop-sensor gives more DOF?
If you changed the focal length to achieve the same field of view, that means you maintained the same distance and I'll presume maintained the same aperture. In that scenario, the reason you gained depth of field is because the aperture of the shorter lens (which is physically proportional to the focal length) is physically smaller than the aperture of the longer lens and the sensor is optically closer to the optical focus node of the lens.
Light isn't affected by the size of the sensor, but it is affected by the physical size of the aperture and the distance from the optical focus node of the lens, and you changed both of those factors. That gives you more depth of field.
If you shoot with the same lens on both cameras (same scene, same shooting position, same f/stop) and then crop the FF image to equal the FoV of the 1.6 crop-factor sensor will you have the same DOF?
This introduces another factor that someone above alluded to. Depth of field is not fixed by the shooting circumstances, but is also affected by the degree of enlargement to the final display size.
We saw this all the time working with film--we'd make a contact print that look pleasingly sharp, but when we enlarged the image--dang, it was out of focus. Of course, you can see it on your monitor as well.
This introduces a new term: Depth of focus. Depth of focus is not to be confused with depth of field. Depth of focus occurs at the sensor. Without going into detail (you can Google "depth of focus"), depth of focus is locked in upon capture. It represents, if you will, what depth of field would be if you did not enlarge the image at all from the sensor dimensions, but viewed it at normal reading distance just as it was projected by the lens.
Once you begin enlarging the image, the resulting depth of field will be less than the depth of focus, decreasing directly according to the degree of enlargement. That includes the increased enlargement resulting from cropping, whether "cropped" by the fact of a smaller sensor or cropped in post-processing.