I thought I had replied to this but seem not to have pressed the right button.
My rough experiments suggested that there is a small difference between the diminished DOF from distance and that from focal length, but further investigation suggests that this might be more perception than reality. If you select one of the objects in the wide view, and magnify it so that it is the same size as that object in the long view, the two images appear about the same. I will try to do some more precise testing to see if it's really the same, or just close, but at least for the present I must modify my previous comment, and go with F-starter on this.
However, one can also say that as we actually see the image on sensor or film, there is a difference in what gets into the image. While we can say that the seemingly clearer objects in the wide view become blurrier when magnified to equal those in the long view, and thus are optically equivalent, it's also true that those in the long view are already magnified in the camera, and that choice of perspective and magnification has affected what we now see. It's all in how you slice it.
I thought I had replied to this but seem not to have pressed the right button.
My rough experiments suggested that there is a small difference between the diminished DOF from distance and that from focal length, but further investigation suggests that this might be more perception than reality. If you select one of the objects in the wide view, and magnify it so that it is the same size as that object in the long view, the two images appear about the same. I will try to do some more precise testing to see if it's really the same, or just close, but at least for the present I must modify my previous comment, and go with F-starter on this.
However, one can also say that as we actually see the image on sensor or film, there is a difference in what gets into the image. While we can say that the seemingly clearer objects in the wide view become blurrier when magnified to equal those in the long view, and thus are optically equivalent, it's also true that those in the long view are already magnified in the camera, and that choice of perspective and magnification has affected what we now see. It's all in how you slice it.
In support of what you say, most DOF field calculators, if you take the same settings except set one to full frame and another to crop, will give different results, because the acceptable circle of confusion changes as you magnify the blur with resizing.