Originally posted by Ikarus ... one would use the same shutter speed as for APS-C and ISO' = ISO * 1.5^2.
... which in turn means that, by virtue of the smaller light
intensity being offset by a proportionally larger sensor area, that the total amount of light on the sensor will be the same between both formats for a picture with the same shutter speed, same perspective and same resulting depth of field. Thus in turn you will have
roughly the same noise level, referred to the entire picture (for assumed equal efficiency of the sensors).
What you gain from a bigger sensor are
options. With a bigger sensor you can work at shallower DoF at the same F-stop if your (longer) lens offers it, thus capture greater total amounts of light and this way improve noise level, or be further away from being diffraction-limited when stacking macros etc.