It sounds like you're describing "Prince of Persia: The Two Thrones," which is part of the Sands of Time trilogy. This game features the Prince grappling with the consequences of his actions and the emergence of the Dark Prince within him. Here are some highlights of the game based on your description:

Dual Characters: Play as two distinct characters—the Prince and the Dark Prince—with unique combat styles, abilities, and personalities.

Combat Options: Utilize the Free-Form Fighting system to engage enemies creatively, employ the Daggertail for ranged attacks, or utilize stealth tactics for surprise takedowns.

Dynamic Environments: Navigate through diverse locations in Babylon, including rooftops, streets, and underground passageways, adding variety and challenge to gameplay.

Storytelling: Immerse yourself in a captivating narrative filled with twists, tension, and character development as you uncover the mysteries of Babylon and the Prince's inner conflict.

Time Manipulation: Employ the Sands of Time powers to control time during combat, allowing for strategic advantages against enemies and adding a unique gameplay element.

Blend of Gameplay: Enjoy a mix of action combat, platforming agility, and puzzle-solving, characteristic of the Prince of Persia series, offering a comprehensive and engaging gaming experience.

If you're interested in playing this game, make sure your system meets the necessary requirements for optimal performance and enjoyment.