From a political standpoint, there was a "change" in terms of the federal government. Jefferson himself meant that his election represented a return to what he considered the original spirit of the Revolution. In his own viewpoint, Hamilton and Adams had betrayed the ideals of 1776 and 1787. His mission, as he saw it, was to restore the republican experiment, to check the growth of government power, and to halt the decay of virtue that had set it under Federalist rule. The Federalists quietly accepted their defeat in the election of 1800 and "peacefully" relinquished control of the federal government to Jefferson's party, the Democratic-republicans. This "bloodless" and "non-violent" change defined the election as the Revolution of 1800. This was an achievement for a young nation like the United States. It was an achievement in the sense after all the partisan bitterness that agitated the country during John Adam's presidency. It was also an achievement in which Britain couldn't accomplish for another generation. After nearly 10 years of doubt and division, American was allowed to take pride in their experiment for democracy.
Judicially, there was a change in regards to the Marbury vs Madison case, and judicial review that developed because of it. During the case of Marbury vs Madison