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Consider two cameras with the same resolution (let's say 640x480) and focal length (or FOV) looking at the same subject. Let's assume that the subject is in focus in both cameras.
Will the image of the subject be the same size across both cameras? That is, if one camera shows the subject as occupying a grid of 10x10 pixels, will the other camera give the same result?
Are there other properties that will affect this?
Apparent size of subject...Will the image of the subject be the same size across both cameras?
IMO, there are three different answers. Which one is correct depends on what you think "apparent size" means.
If two cameras photograph the same subject, from the same distance, using the same lens, then the actual size (measured in millimeters) of the image on the cameras' sensors will be the same. This will be true regardless of anything that you can say about the sensors.
Is this what you mean by "apparent size?"
If the two cameras have different size sensors (measured in millimeters), then the image of the subject will fall on a smaller fraction of the available sensor area in the camera with the larger sensor. This will be true regardless of the pixel densities of the sensors.
Is this what you mean by "apparent size?"
If the two cameras have sensors with different pixel densities (measured in pixels per mm), then the subject will cover more pixels in the camera with the higher pixel density. This will be true regardless of the size of the sensors.
Is this what you mean by "apparent size?"
If the two cameras have sensors with different resolutions (measured in number of pixels), then see above. Resolution, pixel-density, and sensor size are not all independent variables. If any two are known, then the third one also is known:
size_in_mm x pixels_per_mm == size_in_pixels
If you only know the number of pixels in the two sensors (i.e., if you don't know sensor sizes and you don't know the pixel densities,) Then the question cannot be answered.
The size of the projection of the subject on the sensor plane will be the same since the lenses are identical. So it all depends on how many pixels the sensor has to cover that size, which is down to sensor pixel density.
For instance, assume two sensors,
If the image of your subject is 1mm on the sensor, then the first sensor will make it 10pixels and and the second 20pixels.
A corollary is also that the 32×24mm sensor has a smaller field of view (the same subject takes more space on the sensor) or that the same lens "brings things closer" on the smaller sensor.
Both will deliver the same resulting image (10x10 subject) and there are no other factors that will affect that.
That is because you specified cameras with equivalent fields of view; the camera/system FOV is a combination of the sensor size/imaging area and the lens' magnification. A smaller sensor will use a shorter focal length for the same FOV; that's where the "35mm equivalent" focal length comes from (the stated focal length(s) for cameras w/o interchangeable lenses).
And you specified equivalent pixel resolution... which means if one sensor is smaller, the pixels are also smaller.
Smaller sensor, smaller pixels, and less magnification equals the same result in terms of composition and pixels per area. But the two images will not be the same in other ways, such as light per image/area.
With the same FOV and the same number of pixels on the sensor the other propertie(s) you need to consider are lens distortion. Computer vision systems will use a checkerboard to "calibrate" the camera. Generally a wider angle will have more distortion than a narrower FOV. The "projection" of the image is onto a flat sensor. In a pinhole camera with constant sized pixels on a flat sensor the angular density, and therefore apparrent size, will be different near the center compaired to at the edge.
