Handwaving:
- With two drivers (+ and -), a differential signal (XLR) is twice a single-ended signal's amplitude so a gain of 6 dB.
- The two drivers each add noise, but uncorrelated with each other, so do not add linearly but RSS (total noise = sqrt(N+^2 + N-^2), a noise increase of 3 dB.
- Thus you have a net SNR improvement of 3 dB.
Some designs cut back on signal levels or attenuate the input of a differential signal so you may not always see an advantage. Balanced also offers common-mode noise rejection and the ability to isolate the shield from the signal path, providing greater rejection of external noise, and making it easier to break a ground loop.
But, a single-ended design can have a lower noise floor, since there is only one driver and in any event noise floor and signal amplitude can be designed differently for different circuits, balanced or single-ended, so you cannot really draw a general conclusion about one or the other having a lower noise floor. A lot of high dynamic range (120+ dB) RF gear is single-ended, though most serial data links (Ethernet, PCIe, SATA, SAS, USB, etc.) are differential.
HTH - Don