How did Hamilton's and Jefferson's different experiences relating to the writing of the Constitution affect their roles as members of Washington's Cabinet?

Both men foresaw the US as a great future power. However, they differed on the path the nation was to follow in achieving this role. While Jefferson preferred an agrarian nation, Hamilton favored an industrial and business intensive nation. As such, Jefferson detested Hamilton's idea of a strong federal government. Jefferson wanted the bulk of power to rest with the states. While Hamilton distrusted popular will and believed that the federal government should wield considerable power in order steer a successful course, Jefferson placed his trust in the people as governors. These major views were behind polarizing Washington's cabinet into two distinct factions. Hamilton's followers became known as Federalists and Jefferson's Democratic-Republicans. Hamilton and Washington were already close to one another so it makes sense that Washington gave Hamilton the attention he did. More than anything Hamilton's views were prized by Washington; he very well may have been the most socially liberal and economically liberal man of his time, Jefferson stood to counter this with ultra-conservative views and policies. The idea was for there to be a sort of balancing act with the cabinet and it worked out quite well for Washington and the united states. Perhaps because of their differences of opinion, Washington made these two men his closest advisors.