The Unites States government was designed to prevent any branch from gaining more power than the other in a system of checks and balances
The federal government has three branches, and all state governments are modeled after the federal government and have the same three branches. These branches are the legislative, executive, and judicial branches, the manifestation of separation of powers.
Anyone could make an argument that any branch of the government has the most power if taking into account historical context or current affairs, but if the structure of the government itself is taken at face value, then each branch is specifically designed to hold an equal amount of power.
For example, Congress (the body that leads the legislative branch) will write and pass a law, but that law cannot go into effect if the President (the leader of the executive branch) vetos, or rejects, that law. In that instance, the President would be exercising his power over the legislative branch.
Another way that a President can exercise power over the other branches is through an executive order. Executive orders, while not explicitly stated in the Constitution, are implied in Article II of the Constitution regarding the President's responsibility to command the armed forces of the United States. An executive order allows the president to instruct the government specifically how to function within the parameters set by Congress and the Constitution. The Supreme Court (the body that controls the Judicial branch) has the power to declare any Executive Order unconstitutional.
A historical example is when Harry Truman issued an executive order to seize control of private steel mills during the Korean war; the Supreme Court ruled the order unconstitutional because the President did not have the authority to seize private property.
Using context, one might argue that the executive branch has the most power, but the government is designed to distribute power equally.