The League had a small numerical nation advantage, as well as a nuclear advantage. However, from memory, Aegis was clearly outnumbered in both strength and nations; LUE had been kept in a perpetually weakened state, NAAC and GATO had not fully reconstructed, and so on. Though, I should note I'm including all those alliances outside of The Initiative bloc that joined their cause in those numbers, not just the signatories of the bloc itself.
I could be wrong on Aegis and the Third Great War, though. By that time, I was rather fed up with the game (mostly as a result of the stupidity displayed during the Second Great War) and it was obvious from the beginning that Aegis would be defeated, so I didn't bother mentally recording much of the statistics. Besides, I was far too busy kicking Heft from Aegis IRC headquarters and saying "I told you so." to Legion and ODN.