But a sensible photographer will not use the same focal length with a crop sensor than he would with a full frame sensor. . A sensible photographer will frame the image the way he wants it framed regardless of which sensor his camera has. . When an image is framed the same, the larger sensor will produce a shallower depth of field.
Will it? Go back and watch the video again. When he shoots the bear at 80mm on the FF to match the 50mm on the crop sensor, it doesn't look nearly as good. In fact, it looks weird as the lights in the background become giant and distracting. Here is the shot. The APS-C is the superior of the two shots with a more shallow DOF with the exact same framing. I get the feeling people are confusing the background blur and bokeh with DOF. Yes, the FF shot is a bit more blurred with nicer bokeh, but it has a deeper DOF, meaning the subject is not as isolated from its background, it looks closer to the tree. On the APS-C shot, the subject looks further away and more isolated from its background and that tree, its a more shallow DOF.
forum: Camera Vs. Camera
If you stop down the lens on the FF from f/2.0 to f/4 or f/5.6 (which increases its DOF; you understand that, right?), you'll see that those "giant and distracting" lights will look very similar to the ones on the APS-C shot at f/2.0. Since you had to change settings on the FF to increase its DOF to get similar output, it should be obvious that the FF at the original f/2.0 setting had LESS DOF than the APS-C at f/2.0. I have no idea why you think the reverse is true.