How did Alexander Hamilton's political philosophy differ from that of the other founding fathers?
Of course, Hamilton's political philosophy was not different from that of all the other founders. Hamilton was a Federalist like many others. He may have been a bit more extreme than some, but he was not completely different.
Hamilton did not believe in democracy. He felt that there were some people who were naturally fit to rule and the great mass of people who were not. He believed that the mass of people could not be trusted to do what was best for themselves. If given democratic self-rule, they would push for laws that would not be good for the society as a whole. Therefore, Hamilton did not want democracy. He even suggested that George Washington might rule as a king.
Hamilton wanted a government that was insulated from popular pressure. He wanted a strong federal government and he wanted provisions like the Electoral College to keep distance between the people and the government. In this, he was different from the anti-Federalists, but not that different from most Federalists.