Both documents declare that humans possess certain natural rights that cannot be infringed by anyone, not even the government.
The U.S. Constitution establishes the U.S. as republic, where government is a public matter, and is bestowed to the wishes of the people.
The Constitution also gives citizens the power to remove the goverment in case it becomes incompetent or tyrannical.
These are all deeply democratic ideas that can be traced back to Ancient Greece and Rome, as well as the Magna Carta, and the ideas of philosophers such as John Locke, and Montesquieu.
