Normal
Normal difficulty is the default difficulty level. All of the other difficulty levels are modified relative to the Normal difficulty. Player and enemy units all function according to their actual stats with no modifiers. This difficulty level is designed so a player of average skill should be able to beat the campaign.
Easy
The Easy difficulty in "Halo Wars" functions rather differently from other games in the series. The main difference is that enemies have significantly less shielding and health, making them easier to kill. Enemy weapons also do less damage. In "Halo 3" and "Halo: ODST" you could not earn most achievements or unlockable items while on the Easy difficulty. "Halo Wars" does not follow this rule. You can earn every achievement not specifically restricted to Heroic or Legendary difficulty levels and find every unlockable item while playing on Easy. There is no score reduction for being on Easy, which makes it the best difficulty level for getting high scores.
Heroic
Heroic is slightly more difficult than the Normal difficulty level. The most notable change is enemies can take more damage and do more damage. Unlike "Halo 3" and "Halo: ODST," there is no score bonus for playing on Heroic. Some achievements you can only earn while playing on Heroic. This difficulty level is designed to be beatable on the first play-through by an above average skill player.
Legendary
Legendary is the hardest difficulty level in "Halo Wars." The bonuses enemy units get to health and damage is further increased. Selecting this difficulty level also causes additional enemies to spawn, including Shades and Mega Turrets, which normally would not show up in most missions. The AI is more aggressive, attacking much earlier than normal. There are several achievements that you can only earn by beating the game on Legendary. There is no score bonus for playing on Legendary.