There has been a lot of discussion here, including DoF calculations, but amazingly no one has mentioned a very important point with medium format, that contributes to the "look" and has all to do with
film.
Film doesn't have a constant MTF curve. The cycles/mm (resolution) it can resolve decrease rather sharply. For example Fomapan 400 has lowers down to 50% MTF at about 25 cycles/mm and then it goes down on a cliff. 100% MTF is achieved only from 0 to 10 cycles/mm.
Lenses also have a MTF curve of course, which also decrease sharply after a certain point. When you multiply the MTF (modulation transfer functions) of the lens and the camera, you have the system MTF. Lenses are not perfect.
Lenses for pro Medium Format cameras are in general better corrected than 35mm lenses. For example, an 80/2.8 lens for 6x6, done with simply 4 elements (tessar formula) could give perfectly fine results. Even a three-element 80/3.5 can give really good results in 6x6. However, the pro 6x6 cameras have a 80/2.8 of six elements. This means much better correction of abberations and a better MTF too.
Lenses in MF are often of smaller relative aperture and every lens designer will tell you that, everything else equal (focal length, cost target, technology, glass type availability), a slower lens can be much better corrected. Even half a stop slower will make a big difference in the amount of correction that can be obtained. Consider for example a 150/4 lens in 6x6. This will give you an image more or less equivalent to a 85/2 in 35mm cameras, in terms of depth of field and angle of view. Yet, the medium format lens is f4 and thus can be better corrected.
Now, 10 or 20 cycles/mm, in medium format, means much more detail than 10 or 20 cycles/mm in 35mm...
What does this all mean? Combine the fact that 10 or 20 cycles/mm convey finer detail (with greater clarity) in MF, with the fact that the MF lenses are better corrected, and this means that the system MTF curve of a medium format camera is able to resolve finer detail with greater clarity. I'm not talking about resolution alone, i'm talking about MTF which takes into account contrast and resolution.
This greater clarity increases the visual perception of "narrower DoF", since the subject is reproduced with an increased crispness. There is an increased "3D look" because of the main subject being reproduced with greater clarity.
Better corrected lenses also mean better rendering of out of focus areas, for example the "bokeh balls" won't turn into rugby balls at the edge on a better corrected lens. Or won't reproduce as soap bubbles (overcorrected sperical aberration). This is just an example -- but in a better corrected lens the overall rendering of out of focus areas will be better.
So, friends, the combination of all of this is what makes the "medium format look" and it can further be appreciated when optically printing MF pictures.
Yes, digital. Because on a digital camera, the sensor's MTF response is almost ruler flat. This makes the system MTF a lot higher. But this is a film forum. Film, with its peculiar MTF curve, is what makes the difference.
This post is dedicated to
@wiltw .