Leguna pretty much nailed it precisely, but I’ll chuck my two penneth in.
Alliance certainly has the moral high ground. At times they have dragged themselves low, then picked up again, but -generally- speaking, they are not the expansionist power some Horde leaders have thought they were. During WC3 there was a bit of that going on, and during Cataclysm they did go all ‘Manifest Destiny’ on the Tauren, but in general, they are a non aggressive group.
The Horde however, started off with the absolute low moral ground, and on occasion does raise itself up, only to tumble again. It isn’t (As a body politic, not just the individual races) inherently an ‘Evil’ organisation, but equally it has a much more “The Ends justify the Means” mentality, which have led to some bleak actions being taken in it’s name. Both sides have done good and bad, but the Horde has done far more of the bad.
This has now all gone out of the window, with the recent events.
The Horde has (finally!) abandoned the Warchief system that was shackling them to genocidal maniacs recently, and what we seem to have is a Council, that was instated by a Triumvirate of leaders, (Baine, Lor’themar and Thrall) that every other race agreed with.
Ironically if we were to look at this through modern eyes, the current Horde rulership is a more enlightened one than the Alliance one.
Whilst Anduin is a good boy, his absolute monarchy, as liberal and benevolent as -he- is, could set the precedent for a repressive rapacious tyrant to succeed him with those powers, Whereas the Horde rulership kind of makes sure that unless -all- the council are maniacs, that such things would be kept in check, and not possible.
Given that they formed the Council to step away from the idea of a bloodthirsty Tyrant controlling everything, and the longevity of two of it’s Council members in term of lifespan, they’re not likely to forget that fact.
So the Horde has a more enlightened and representational form of Government than the Alliance, however with past deeds, the Horde is definitely on the back foot when it comes to morality.