sensor - Reason why MFT are less bright than FF cameras?

My understanding is that low-light performance is a function of the amount of light received on the sensor per unit area (correct if wrong). If this is the case, wouldn't an MFT system have the same light sensitivity of a comparably proportioned FF system? For example, if using a 50mm/1.4 lens on a FF and a 25mm/1.4 lens on the MFT, the FF will gather four times as much light, but it will spread that light over a sensor that is four times as big, so won't the amount of light per unit area on the sensor remain the same?