Strategically, it doesn't get more intense than Blizzard's StarCraft II: Wings of Liberty, especially in the game's multiplayer component. Players dance back and forth between attacking, expanding, harassing economy and supply lines, all while carefully advancing up expensive tech trees in a constantly evolving meta-game.
In the campaign, players face multiple objectives per mission and choices to make at almost every stage of the game, which determines the units, upgrades, and bonuses a player will gain throughout the course of the campaign. Each mission has its own unique mechanic, which creates a varied experience from start to finish that requires a different approach to each level.
Runner-up: Sid Meier's Civilization V
Civlization V brought a much-wanted revamp to Civ's combat, making it more complex than simply stacking up powerful units. With unit stacking removed and ranged truly able to attack from ranged, it's far more interesting when diplomacy fails. Plus, Giant Death Robots. Autonomous city states are a welcome addition to the diplomatic side, courting the attention of all players while offering useful rewards.
I had more fun playing Dawn of War II than I did Starcraft II singleplayer but DoWII was closer to Diablo than Starcraft in the SP so it made the story feel a lot more epic.