Quote: On my screen, the nose looks to be pretty much in focus on the Full Frame version. Less so on the 2/3 Full Frame, and definitely distressingly out of focus at 1/3 Full Frame. All that's changed here is the smaller sensor needs to enlarge the dogs face more to get the same final print size. This makes the blur that already exists on the nose less and less tolerable since this extra enlargement magnifies it.
Now that's what you've got messed up.
FIrst of all, if your dogs nose was in sharp focus and you had a good sensor, it would still be in sharp focus on the enlarged image. I have foveon images taken with my DP2M, that look just as good enlarged to 1:1 as they do small. So that is defintiely a technical shooting issue, not per se a function of enlargement. Second. If your crop image was taken with a 24 MP crop sensor, you'd have about 30% more resolution in the crop image.
Your comparison is accurate in that for DoF we are discussing at what point the circles of confusion become visible. And that requires a lot more work than what you're doing here. So as long as the images are sharp, as in a circle of confusion less than one pixel, sharpness is determined by the number of pixels in the frame. In that case, APS-c kills any FF less than one with at least 50 MP, and those (like unicorns) don't exist.
At some point you would have to do research to find out at what point the circles of confusion become visible in your print. There are many factors in this as well. My own meager fooling around deduced that at 3000 pixels across, a K-5 image was indestinguishable from a D800 image on a 92 pixel per inch screen. That translates to roughly a 30 inch print , printed at 100 dpi. At some point the amount of magnification of the circles of confusion become more of a factor. So what I'm saying is , at 1:1 magnification of the image, that is the FF image is 33x22mm, you wouldn't see the difference in size of the circles of confusion. You have to magnify quite a bit before the difference in DoF even becomes visible. I'd assume once the DoF becomes visible at some point you would start measuring the distance in DOF, but what the defining parameters would be and how they would be applied would still have to be determined, and the results would depend in part on the visual accuity of the viewer. So honestly I'm not sure what you hope to gain from this. ALl you really need to know is you can achieve narrower DoF with an FF camera and with an equivalent lens wider DoF with an APS-c camera. If you are limited by not getting narrow enough DoF, then shoot full frame. If you are a hyper focal shooter and are limited by too narrow DoF, shoot APS-c. Beyond that, making precise calculations of DOF to determine the DOF on various systems is pretty much a waste of time. The resulting measurements won't be accurate enough to justify the math. You learn a lot more from trial and error.
To me, the biggest factor in narrow DoF images is, how smooth the bokeh is, and that tends to be a factor of how corrected the lens is,and has nothing to do with focal length or aperture.