DOF:
Understanding DOF, its connection to aperture, and thus the total amount of light that makes up an image, is critical. That is, for images created with the same shutter speed, the total amount of light making up the image, and the DOF of the image, go hand in hand. Let's begin with its definition: DOF is the depth of field, which is how much depth of the image is in critical focus. It is a subjective measure, to be sure, but is not arbitrary. That is, you can debate what an "acceptable" DOF is for a particular photo, but you cannot debate whether or not two photos have the same DOF -- that can be determined both visually and mathematically. It is important to understand that DOF is a function of many factors. For the same perspective, FOV, output size, and CoC (the CoC scales in the same way as does the focal length and f-ratio scale), the DOF is a function of the aperture, which is the ratio of the f-ratio and focal length. Since we change the FL to get the same FOV for the same perspective, we must also scale the f-ratio in the same proportion (multiply by the FM) to get the same aperture. For example, 25mm f/1.4 on 4/3, 31mm f / 2.5 on 1.6x and 50mm f / 4 on 35mm FF all have the same aperture since 25mm / 2 = 31mm / 2.5 = 50mm / 4 = 12.5mm will all have the same framing and DOF for the same scene. In addition, the same total amount of light will pass through the lens onto the sensor for the same shutter speed. The importance of total light, of course, is that two images of the same scene made with the same total amount of light will have the same quantity of noise if the sensors have the same efficiency.
Furthermore, larger sensors do not reach diffraction limited resolution at the same f-ratio as smaller sensors; they reach the diffraction limits at the same DOF regardless of pixel size. For example, a Canon 5D at f / 16 will suffer diffraction softening no differently than an Olympus E3 at f / 8. Let me explain a bit on the pixel size not being important in terms of diffraction. The smaller the pixel size, the more pixels that can fit on the sensor, and thus the more detail the sensor can resolve. However, with a smaller pixel size, the effects of diffraction will be more pronounced which will exactly cancel the extra detail of having more pixels.
Let's look at some examples of equivalent settings from common cameras (using the same AOV, not FOV):
Canon S3 @ 8.3mm, f / 2.7, 1/400, ISO 80
Canon G7 @ 10.3mm, f / 3.3, 1/400, ISO 125
Canon Pro1 @ 12.7mm, f / 4, 1/400, ISO 185
Olympus E510 @ 25mm, f / 8, 1/400, ISO 720
Sigma SD14 @ 29mm, f / 9.2, 1/400, ISO 950
Canon 40D @ 31mm, f / 10, 1/400, ISO 1125
Nikon D300 @ 33mm, f / 10.5, 1/400, ISO 1250
Canon 1DIII @ 40mm, f / 12.7, 1/400, ISO 1800
Canon 5D @ 50mm, f / 16, 1/400, ISO 2880
Mamiya ZD @ 67mm, f / 21, 1/400, ISO 5120
Note that some f-ratios are impossible since the cameras allow settings in only 1/3 stop increments. This same issue affects ISO settings if shooting jpg, but may be attainable depending on the RAW converter. In any event, we are talking about deviations of less than 1/3 of a stop, which I will disregard as insignificant. If you are so good of a photographer that less than one third of a stop is important, then this essay is a waste of your time! Also, please keep in mind that equivalence does not guarantee the same noise for equivalent images unless the sensors are of the same design and efficiency.