Empirically, a photomultiplier tube (PMT) is said to present better signal-to-noise ratio (SNR) than an avalanche photodiode (APD). Some materials say that it is attributed to the higher gain and lower dark current of PMT.
The benefit of higher gain is confusing to me, since I suppose that noise (from incident photons and from the PMT detector) and signal are both amplified by gain. Why does higher gain result in better SNR?