balanced vs unbalanced

If everything is proper, no difference of sound quality.

Noise is cancelled when it gets on both hot and cold input of balanced system, and that was the main reason balanced input has been adopted for professional system where the input line can be long through noisy environment.

Improvement vs. unbalanced when balanced input is used can be an indication of a poor CMRR (commom mode rejection ratio) of the amplifier. If the amplifier's front end differential stage is perfectly designed, there should be no difference.