The depth of field is the zone of acceptable sharpness in an image. This is a relative value; it is never absolute. Traditional depth of field numbers have been based on a fixed final image output size, namely an 8x10 print, but regardless of the target output size, the principle is the same.
For a 4x5 camera, to produce an 8x10 print, the image has to be enlarged 2x. Anything that looks sufficiently like a line or a point in the print, no matter how "fuzzy" it is on the negative in absolute terms, is deemed to fall within the depth of field. For a 35mm frame to make the same print, the image must be enlarged approximately 8x, so whatever is equally fuzzy on the negative in absolute terms will be four times as fuzzy on the reference print.
Given that the same focal-length lens used at the same aperture will produce the same image on the recording medium, the image that requires the least enlargement will result in the greatest depth of field. If you were to use a 24mmx30mm crop of the 4x5 image negative to produce an 8x10 print, it would require the same enlargement as the 35mm frame and have the same depth of field.
However (and this is a rather large however, as howevers go), it is a very rare occasion when we'd use the same focal length lens on different formats to try to achieve the same image. In this case, you would either be using a 400mm lens on the 4x5, or a 24mm lens (or a 25mm if you can find one) on the 35mm camera so that the resulting image would have the same field of view. At infinity, you would find that the two images would have as near the same DoF as makes no never mind, modulo film grain/sensor density, diffraction and aberrations. But life doesn't happen at infinity most of the time; you have to take into account bellows draw (or the change in focal length that happens when an internal-focus lens is focused closer than infinity) and the way that affects the depth of field.
Digital, too, complicates matters a bit, since there are absolute, discrete steps between things falling entirely within one sensor pixel and spilling over into the next. The pixel-peeper's circle of confusion is fundamentally a different beast from the film shooter's circle of confusion. (Personally, I'd love to see the day when resolutions are so high that pixel peeping becomes an exercise in futility; it would put an end to a lot of the utter silliness that currently pollutes photographic discussion.) As well, the size of the sensor is not directly related in any way to the pixel resolution of the sensor, so a (hypothetical) 30MP 4x5 "full-frame" digital camera would need exactly the same amount of enlargement as a D800 or an α7R to make the same-sized image, whether printed, projected or displayed on a screen.
Basically, though, it boils down to this: the less you need to enlarge an image, the more fuzziness you can tolerate before things start to look fuzzy.