When one discusses this topic, it should be clear what the goal is. Otherwise we will run in circles.
If the goal is to reproduce the same photograph (same perspective, same field of view, same DOF, same motion blur (implies same shutter speed) with two formats (using the full frame without cropping) and display them both at the same size, then the exposures must be different for the two formats. The photographs will have the same brightness and noise level if the ISO is chosen appropriately for each format (different ISO for different formats).*
- What does it imply for the importance we should place on exposure in this context?
- Does anyone disagree that the two photographs look the same under any circumstance or with any viewing device?
Does anyone disagree that we can deduce from the above that if the exposures are the same for the two formats, we either get
- different DOF or
- different motion blur,
but we definitely get
- different noise levels,
- the same perspective.
(it is assumed that ISO is the same here such that image brightness is the same).
The noise amplitude is lower for the bigger format and the information theoretic reason for that is that more photons were collected by the bigger sensor if both sensors were exposed the same (same energy per unit area).
* All these considerations are made under the simplifying assumption that sensor technology is similarly mature for both sensors and that things like the exact architecture or number of the photosites are similar enough to be neglected. We also assume that we can find lenses for each format that project geometrically similar images and are diffraction-limited. All statements are approximate to the extent that these assumptions are violated, but they shouldn't usually be violated by orders of magnitude.