Not really, to take the
same photo with two different cameras using different size recording media the camera with the smaller sensor/film will produce deeper DOF all other factors adjusted so as to produce the
same photo. No comparison is otherwise appropriate except one in which you use the two cameras to take the
same photo.
To take the same photo both cameras must be in the same place. The field of view at least against the long side of the media (assuming possible different aspect ratios) must be the same and the exposure must be the same.
Joe
View attachment 130472
I really do not hold with this "equivalence", or same photo nonsense, (in fact it annoys me

), because it's so meaningless and misleading.
If in your instance you hold
exposure (or same f-stop) as constant and to satisfy the condition of
the same photo you also have changed the focal length and the amount you magnify the finished image to the final print. The sensor size does not change the way the light passes through the lens, it's only affect on dof is the amount you have to magnify it to produce the final image.
Take for example the following case which is encountered in normal photography:
You take a photo with a camera and a certain lens, you print it 10"x8". You then crop it, (after the brilliant advice you receive off this site), and print again at 10"x8". How does that affect the dof? Are you going to tell me that the case is irrelevant because it does not satisfy the condition of
the same photo? Of course not.
The whole system of exposure/fov/dof is very symmetrical and if you hold some things constant then others cancel out. In equivalence where you take the same photo (and same dof) with a different sensor is a very special case where a number of variables
must be held constant. In this special case a number of other variables cancel out.
To explain, in order to satisfy the condition of
the same photo (with the same dof) then subject distance, fov and
aperture diameter in mm must be held constant. In this instance
exposure must vary but focal length cancels out of the equation. But we do not take photos like this.
In your case you substitute
exposure for
aperture diameter in mm but still insist that other things must be held constant such as fov and subject distance and the conclusion is that sensor size affects dof, which it does not directly do. A fuller understanding is that with smaller sensors you use shorter focal length lenses and to maintain exposure you are using a smaller
aperture diameter in mm which results in the increased dof, it happens before it reaches the sensor and happens when you use shorter focal length lenses on the same sensor.