it was the competition between Thomas Jefferson, and Aaron Burr.
Jefferson wanted the people to have all the power. As for Burr, he was very much like Hamilton, in fact, they were very close friends in life too, but mostly due to the fact that they agreed in political parties which caused no conflicts. Hamilton's belief was that all the power belonged to the government, and the world should be made of business. Both people believed this was the way to a utopian society and this was going to make the country in succes.
Hope this helps somewhat ;-;