What's the advantage of balanced outputs?

I'm not familiar with these particular speakers, so I may not have all the facts pertaining to them. However, in general, balanced is preferred for long runs. Because the live poles are operating out of phase there is a noise cancellation with balanced runs. It is important to note that balanced circuitry is more complex, expensive, and sometimes not executed very well. Some companies add balanced outputs to their products simply for marketing reasons and do a poor job executing them. In this case, any advantage balanced might buy you will be eaten up by just poor circuit design or execution. However, when balanced is done right and you have long cable runs (typically from pre-amp to amp) then balanced can be a real benefit. In your case if the M&Ks amps are REALLY designed for balanced inputs and you have reasonably long runs, then it makes sense to go balanced.

What's considered a "long" cable run?

I would consider long being more than 3 meters. But long is a relative term, and if you are in an area with a lot of RF interference, then the advantages of balanced might be noticable at only 2.5 meters. On the other hand if you are in a low RF area then you might be okay up to 4 meters.