Rubberhead wrote in post #5134188
I have 20/15 vision and have never needed glasses or contacts so I don’t have any trouble setting the diopter on my camera or the dipoter ring on my binoculars. However, if I was to put on my wife’s glasses and set the diopter, I would, at best, see a very blurry image and I doubt I would be able to set the diopter as well as I could if I used my 20/15 vision even though all I had to do would be to chose the setting that gave me the less blurry image.
If it makes you feel any better, I (think) I understand the question you're trying to answer, and I think your analogy makes sense. In essence, you're asking if it is better to have more light (via a wider focusing aperture), or to have a sharper image (ie. using a lens with a smaller maximum focusing aperture), available to the camera to make a focusing decision.
So far I think all of the responses have contained correct facts but haven't completely addressed this question. I can't claim evidence one way or another, but I think you have to take in to account the difference in available light in your diopter analogy, as your eyes naturally adapt their 'aperture'. I think that having a full stop more available light for focusing at f/2.8, and doubling the number of contrast sensors at that aperture, more than compensates for the increased sharpness available from a f/4 lens, especially considering the AF is looking for the 'best' contrast at the centre AF point and not necessarily optimal 'sharpness' throughout the whole image.