It has nothing to do with the length of the cable.
All commercial solid state amplifiers have balanced output stages (with the exception of a few of Nelson Pass's esoteric products, which are single-ended). In other words, two amplifier output stages do the work of one, each one of the positive and negative phases of the audio signal, and then when the outputs of the stages are combined for the speaker output common mode noise and distortion are cancelled. Quad-balanced is a topology where two balanced amplifier stages are used for each of the positive and negative phases, so four stages doing the work of one, supposedly further reducing noise and distortion by increasing the common mode rejection ratio.
Fully balanced means that all of the amplification stages in the amplifier are balanced. In most amplifiers there are three gain stages, and usually only the output stage is fully balanced. At lower voltages and currents the advantages of common mode cancellation are reduced. In some expensive amplifiers, like the quad-balanced McIntosh and the ATIs I use, all of the gain stages are fully balanced. So if you feed a fully balanced amp with a balanced signal there is end-to-end noise common mode cancellation, which supposedly improves sound quality. As Gene has pointed out, the improvement is measurable, but I think audibility is another question.
To be honest, I have a conventional amp (balanced output stage only) and a fully balanced amp from the same manufacturer, and if I don't clip the lesser amp I can't hear *any* differences in sound quality. Balanced circuitry can measure better, but I'm not convinced fully balanced circuits are necessary for the best available sound.
I should also mention that I'm not a fan of McIntosh solid state amps, because they have useless output transformers that simply add cost, weight, and complexity, and increase the output impedance of the amp. They also reduce available power into low impedance speakers, when I think many modern speakers designers count on solid state amps to provide more power at lower impedance. (Of course, at McIntosh power levels I'm probably making a moot point.) Yeah, they are awesomely built and look great, but those output transformers (autoformers) are about as much use as the batteries on some Audioquest cables, IMO, so they bug me.
