I don't agree with this "amount of light" argument. Consider a full frame sensor and an APS-C size sensor with pixels the same size as a full frame taking photos with the same lens at the same f-stop and the same distance from the subject. The signal to noise ratio for each pixel in the APS-C sensor will be the same as the S:N ratio as the corresponding pixels in an APS-C sized area of the ff.
True, but the 2.56x greater area of the FF sensor will gather more total light. Comparing noise at the pixel level isn't the same as comparing noise at the image level.
You lost me on the image level noise, Neuro. It seems that an APS-C sized crop of the FF image and the APS-C image in this case would be identical. The number of photons hitting each pixel is the same and assuming the downstream operations are identical, what's the difference?
I don't know about you, but as a photographer, I strive to compose correctly, and I look at the image as a whole myself. Your above scenario doesn't make a huge amount of sense as the resulting photos would be very different. I'd start off by using an appropriate focal length on each format to capture the chosen image, not to mention choosing an aperture to achieve the desired DoF, and an ISO to achieve the desired shutter speed/exposure.
If you truly do use the same length lens, settings and distance from subject with the larger format, it would require cropping in post to achieve the framing you've strived towards with the APS-C body. Now we're left with the same image as an APS-C body would have taken - just under 40% of the image. In other words, just under 40% of the light. So to enlarge this small crop up to the same viewing or printing size that you would have wanted should the whole frame of that FF body have been filled correctly, you've now magnified what signal is left by 2.56 times. And strangely enough, the noise has been magnified by that exact same amount too.
If we could just keep cropping with no enlargement penalties such as additional noise, why would anyone bother with these huge telescopes in Hawaii? Surely we can just equip the optics in an iPhone with a sensor 10,000 times smaller than the 1/3rd inch sensor they currently have? We could see the most distant galaxies with unimaginable magnification and clarity, all from a device in your pocket? After all, it is an f2.2 lens