I think the noise you are describing is the inherent self-noise of the mics. Normally, that's not audible because the level of the signal is so much higher. In this case, though, the signal is low so the self-noise becomes more apparent. More sensitive mics will pick up more signal, so they will more effectively drown out that self-noise (assuming similar self-noise levels). They will also pick up more ambient noise, but in proportion to the music level, so that won't be any more audible.