This is total nonsense, you do not get an expansion where each faction gets to "shine" or the story is more "focused" on them. The story just advances and each side ebbs and flows.
And the Orcs were VERY much the underdogs in Warcraft III. The Horde was shattered, the Orcs were just a handful that managed to escape from internment camps and flee across the ocean. In fact they spent the whole game in retreat until Medivh convinced Thrall to fight the Legion in Hyjal, alongside the Night Elves. In the expansion they didn't even have a bloody role in the main plot, we got a solo RPG experience centered on local Kalimdor events instead!
P.S. In response to your sig, the Alliance of Lordaeron was formed out of Azeroth (now called Stormwind - in exile as it did not at that time exist as a nation), Stromgarde, Kul Tiras, Gilneas, Dalaran and Alterac and eventually their allies in Quel'Thalas and Khaz Modan (notably the playable dwarves in WC2 are actually Wildhammer - well except maybe the Demo Squad which might be any clan) under the command of the King of Lordaeron. After WC3 the Alliance of Lordaeron was destroyed - the nation of Lordaeron was annihilated by the Scourge, Dalaran was destroyed (eventually rebuilt but was neutral until just recently), Kul Tiras and Gilneas dropped off the face of the earth (until Gilneas rejoined the Alliance in Cata) and Alterac betrayed the Alliance and was obliterated. Stromgarde somehow got itself wiped out by Ogres and thieves.
The new Alliance - the "Alliance of Stormwind" I suppose - was formed years later by a rebuilt Stormwind. It was under the Kings of Stormwind, a totally different dynasty to the Kings of Lordaeron. Not to mention on the other side of the continent. At WoW release none of the other six core human nations of the old Alliance were allied with it. Quel'thalas was MIA until BC when it declared itself for the Horde. The Dwarves and Gnomes of Ironforge declared themselves for the new Alliance but the Wildhammer dwarves weren't a part of it until Cata, so that's only a third of the Dwarves (to be fair I don't know whose side the Dark Irons were on in WC2 or if they just stayed in their mountain).
So I think it's demonstrably a completely different political entity. The only link is the nation of Stormwind which didn't exist at the time of the Alliance and some of Khaz Modan. And now Gilneas as it's back in the fold. It's more like the old Alliance now than it was at WoW release, but still.
We don't know what their relative numbers were (unless some non canon RPG book gives those figures), but we do know that Stormwind and Lordaeron were much less militarised than the Horde and the Horde's military push of course was highly successful. At least until the tide turned at Lordaeron City.
Mmm, Silvermoon didn't really have a massive military at the time.
---------- Post added 2013-04-03 at 05:09 AM ----------
Both betrayals of course were necessary so you could play at least one story mission as Horde vs Horde and Alliance vs Alliance