Originally posted by Class A Yes, but that's because exposure is defined in terms of cd/m^2, i.e., light intensity per a unit area. If you keep the exposure constant, the camera with the larger sensor will collect more total light (same light per unit area but there are more unit areas). The increase in total light helps to bring down the noise (the signal to noise ratio, actually).
No, I don't think the larger total light gathering area of a FF sensor helps to bring down noise. Because the total area as such is not the denominator of the noise. The noise starts at the photosite level. The reason, why FF cameras tend to have less noise is, because they single photosite is bigger and thus less noisy. The signal-to-noise ratio of the sensor should not be confused with our perception of noise, anyway - which is a different thing.
And here a larger sensor might bring the exact same advantage into the game, as MF and LF cameras did with film: you need less magnification of the RAW image, when printing to the same print size, as you would need for an APS-C RAW.
Nevertheless, in my personal view the noise topic is not of much interest anymore. The progress in that area has been huge and APS-C cameras do easily fullfill my personal needs in terms of s/r. The only thing, that might bother me, is the increase in DOF and the setting in of diffraction effects, which is both a hallmark of the smaller sensors. That is the reason, why I rarely use a lens, slowlyer than /2.8, except for extreme wide angles, where a thin DOF is a moot point...
Ben