The question here is; DoF being equal for both, would a lesser magnification that needs to be cropped have less image quality afterwards than a shot taken fully closed down? And if yes; how much of that quality is worth the four stops of light that can be invested elsewhere because we shoot wider open?
Absolutely less, for more than one reason. You miss the big picture. You heard stopping down increases diffraction, and that's all you can think about. I heard it increases DOF and improves the image, and that's proved very big with me.
Lesser magnification (including cropping which is a bit different)... but both must be enlarged more to show it the same viewing size. Enlargement is magnification, which enlarges CoC too, which reduces DOF. DoF is judged by how visible the enlarged and viewed CoC appears.
This is why CoC definition is specified as a tiny percentage of the image diagonal (to be proportional to the standard enlargement that it is viewed at... standard so it can be compared). The Carl Zeiss formula is one of the most popular, and it arbitrarily specifies CoC to be (diagonal / 1730). DOF is only about magnification (when viewed). It all fits together well if you know a thing or two.
Zeiss formula - Wikipedia, the free encyclopedia
BTW, some whippersnapper on Wikipedia says 2001, but the Zeiss 1730 value was well known in the late 1950s. This stuff is ancient, it's been known forever.
FX CoC is often given as 0.03 mm. FX diagonal is 45.3 mm / Zeiss 1730 is 0.025mm CoC. But there are several other arbitrary guesses than Zeiss'. It's really just what is imagined visible to the eye at standard 8x10 enlargement (an approximation, but viewed at 10 inches). But there are more facts known than just the notions you make up.
CoC x total magnification is the diameter that becomes visible to us. That is its definition. Thinking people only compare it numerically under the same fixed viewing conditions. Back in the day, doing darkroom work, when we came across a good image, we made an 8x10. It is how we viewed it. Only way we had. Today, we don't print much, but 8x10 at 10 inches is still the standard where the CoC number is defined to be visible. Anything else is just ignorance of the facts. Great as the internet is, it has lost a lot, allowing any idiot to post any stupid thing.
2. and it is NOT equal DOF. DOF is magnification, longer lenses, or shorter distances, etc. Yes, one property can balance the other, and DOF is said equal if the subject object is still same size. But you word it less magnification, and a smaller image always has to be enlarged more, which enlarges CoC too, reducing DOF.
Four stops: If stopping down makes a considerable improvement in DOF, and certainly it can and usually does, if the proper situation (esp macro), then of course it is normally well worth it. Certainly to me it is.
I do understand this discussion is totally pointless. You never consider one detail that I say. You ignore all, and just say meaningless words back. Still, it's kinda fun (and funny), and I have the satisfaction of knowing I'm right (not just something I just made up), and it might influence others who actually think about the facts.
If aperture/magnification is impossible, it implies that when I have a certain amount of light using f/8 at 1/125s, it is simply impossible to get that same amount using any other setting.
You have really never heard of Equivalent Exposures? It is the basis of EV, a chart of multiple setting combinations for same exposure.