The President is to have power, with the advice and consent of the Senate, to make treaties, provided two thirds of the senators present concur. The king of Great Britain is the sole and absolute representative of the nation in all foreign transactions. He can of his own accord make treaties of peace, commerce, alliance, and of every other description
Although the president is the main(or woman), he doesn't have complete say in things like treaties, whereas the king has complete say, no matter how bad the decision may be.