Couple design ideas to inspire players to choose the underdog faction.
Regiment the more powerful faction's gameplay mechanics making the player feel forced and controlled to play a certain way, the loss of freedom will discourage many players who seek freedom as a very important ideal worth fighting for. In addition to the gameplay, the progression could request the player to carry out missions that go against common moral comforts sustaining the factions authority quietly but forcefully.
Visually inspire the player to choose less powerful units. When I played Diablo 2 I played the Necromancer the whole time simply because he was more interesting to watch (no matter how useless he was).
Expanding game play depth of less powerful factions inspire skilled gamers to stick with the underdog often because the more powerful faction quickly becomes boring to play.
Explore the stronger faction in a single player campaign, giving the player every reason to hate them, then offer the other factions as alternatives for multiplayer and single-player hard mode and ultra hard modes.