If we have two cameras, one with a larger sensor that the other, both with sensor systems that we operate at an ISO SOS of ISO 400, [...]Why the same ISO?
Because that gives the same exposure. Of course, since total light gathered is different, image noise at the same ISO is not equal...
... which confirms that the APS-C system in this scenario is "slower", and that was the reason for my remark.
It isn't slower. The total light over the area of the sensor MAY be more finely divided (there is no reason an APS-C sensor couldn't have the same pixel pitch as an FF, or for that matter, larger pixels), but that does not change how fast the whole area saturates at a given EV. If the APS-C sensor was slower
, the exposure value
at a given aperture and shutter speed would be different, yet that is not the case. For any given aperture and shutter speed, exposure value is always the same, as it doesn't have anything to do with sensor area.
The noise increases because the pixels are smaller, not because the sensor, or he lens, is "slower." Back to the same old argument, but shoot the same subject with the same lens at the same distance, crop the FF, and scale the APS-C image to the same size as the cropped FF image. Noise and EV will be the same. Frame the two identically with the same lens, noise will be lower on the FF, while EV will still be the same. The only thing that changed when framing identically is pixels on the subject
of the exposure remains the same.