I run a fully balanced system, because I have power monoblock amplifiers located directly behind each speaker, in order to minimise the length of the speaker cable (< 1m). The power amplifiers, which have a balanced input, are fed by balanced-line cables running back to the preamplifier, itself having dual differential inputs and outputs. The cables are 15m long, running underneath the floorboards.

On a technical level, balanced line connections have the advantage that the signal return is completely separate from the shielding and safety earth. IMO with unbalanced connections, the combination of signal return with the 0V rail and the equipment safety earth, means that minute earth currents can interfere with the signal; which is why, again IMO, some unbalanced cables can sound different to one another.

For the vast majority of installations, I doubt if moving to balanced interconnects would make much of a difference.

If you want to try out using a balanced-line cable, the best place to would be between the source (phonostage, if it has a balanced output, and CDP or DAC). I am in the middle of trying out a number of balanced-line cables between my CDP and preamp, both of which have true dual differential connections, but so far I cannot hear any real and repeatable difference between them; which is what I would expect.