Balanced vs. differential is always an interesting subject in the audio world. Balanced circuits are usually differential but not always, and there is a range of differential circuits from fully-differential to quasi-differential to essentially impedance-balanced designs that aren't really differential at all in the sense I use the term. YMMV.

Ideal differential circuits cancel even-order harmonic distortion and provide common-mode rejection. The amount of improvement is very dependent upon the circuit and application (grounding one side of a differential signal tosses almost all the benefits).

With differential circuits, or bridged amplifiers (not necessarily the same thing), the signal voltage is doubled since you have two amplifiers swinging the signal with one output inverted. Assuming the noise is not correlated (normal assumption, again not always true), it does not double since the noise is not always "in phase" like the signals, so noise increase by roughly sqrt(2). The net gain is 6 dB in voltage and only 3 dB in noise, a 3 dB increase (improvement) in SNR. Plus whatever improvement you get from reducing even-order harmonics and reducing common-mode noise.

HTH - Don