I agree with much of what has been said, and offer a couple of other thoughts that haven't been fully explored. First, for a piece of equipment to be truly balanced, it has often has two sets of circuits for each channel, one for both the positive and negative phase of the signal, as well as a ground (hence, the three pin connection). This implementation sometimes requires more parts (cost) and more accurate part matching (cost, again), but results in performance gains, especially in the areas of reducing or eliminating the need for negative feedback to deal with distortion (as I understand it). It also allows for greater voltage swing potential, or conversely, the capability to create an equal voltage swing with less effort, which may explain why a balanced output sounds (and is) louder. So, balanced interconnects in and of themselves are only part of the story, and probably only really warranted between truly balanced components. And even then, there's some debate! FYI, I run a fully balanced system (BAT) and use balanced cabling throughout.
If you want to really get lost in the debate, visit Audio Asylum and search 'balanced circuit' Oh, make sure you've got lots of time on your hands!