The impact of the Federalists and Anti-Federalists on the Constitution can be seen, respectively, in the extensive powers granted to the federal government and the Bill of Rights.
Federalists believed that the United States should have a strong central government. To a large extent, this was a reaction against the Articles of Confederation, the previous constitutional arrangement that deliberately kept central government weak as a way of defending Americans' hard-won liberties.
It soon became clear, however, that the Articles of Confederation were inadequate for the newly independent nation. Without a strong central government, the United States would not be able to make good on the enormous debts it had accrued during the Revolutionary War. Nor would it be able to resolve territorial disputes with foreign countries.
With that in mind, the Federalists sought to give the federal government a great deal of power, and they enshrined this principle in the United States Constitution. In response to this, Anti-Federalists refused to ratify the document unless certain constitutional protections were put in place to protect states and individuals from an over-mighty government.
In the end, a compromise was reached whereby a series of basic, fundamental rights were added to the original document. These are known as the Bill of Rights, the first ten amendments to the Constitution of the United States. These rights were intended to assure Anti-Federalists that the new Constitution did not represent a threat to the liberty for which Americans has fought and died in their war of independence against the British.