The balanced line is preferred for long cable runs with low level signals because it allows for better shielding and much better resistance to picking up emitted electrical interference.
In a regular, unbalanced guitar cable the signal is carried on a center conductor of your cable. Every circuit needs a return path, and in a regular cable this is the woven or foil shield which surrounds that center conductor. Because the signal level is low there needs to be a shield that will try to carry electrical noise off to ground, and in this case, that shield = ground = part of the signal path. The conductivity of the center conductor and the shield aren't matched so that may affect signal quality (this is part of why long guitar cables lose treble).
In a balanced cable, there's a separate matched pair of wires for signal + and - and they're insulated and twisted together their entire length. There's a shield around that that's completely electrically isolated from the signal carrying pair. So the shield can now intercept electrical noise and shunt it off to a ground which is completely independent of the signal. The signal wires are a perfectly matched pair so the electrical characteristics are more ideal.
The core difference between balanced and unbalanced is something really clever. In an unbalanced system, the center conductor is carrying the signal which is relative to ground. The amp takes that signal and amplifies that, but because any noise that the shield intercepted is being dumped into the ground too the amp will amplify that too.
In a balanced system, the signal comes from the microphone or pickup and goes into one side of a matching transformer. The other side is connected to the signal lines in the balanced cable. Because of the way that transformers work, what comes down the cable is differential; the difference between the + and - wires is equivalent to the original signal and can be recovered by using a matched transformer on the other end. There's a bunch of interesting things about differential signals, but one neat thing is that the transformers can passively change the voltage so it's a higher level signal passing down the wires (which is more immune to noise pickup). Another neat thing is that any electrical interference that's picked up along the way is induces the same absolute signal in both sides of the signal pair but since they're subtracted from each other at the receiving end, that induced noise will be cancelled out (and the shield is more effective now anyway). That's why the signal pair is twisted - even though the two signal conductors aren't physically in the same space, when it's averaged out over a twisted pair, they are effectively equal. It's way cool.
The bad part about balanced connections are that they are a lot more expensive - it will take twice as many conductors in the cable, and you'll need transformers on both ends. For electric guitars, they just didn't start out that way, and haven't really changed since.
I think this actually goes all the way back to Alexander Graham Bell who was a very, clever guy.
David fung