The primary difference between the Declaration of the Rights of Man and of the Citizen and the Declaration of Independence is that the Declaration of Independence proclaimed rights as a sovereign nation, while the Declaration of the Rights of Man and of the Citizen regarded individual people.
The Declaration of the Rights of Man and of the Citizen mainly applied to people of France, while the Declaration of Independence regarded colonists in Great Britain.
Although in different contexts and places, both documents stood for liberties and rights. They shaped our history and the foundations of our countries today.