Federalists believed that there should be a strong central government. They believed that there should be a national bank and a constitution. Most of them were lawyers, bankers, and merchants (wealthier people). George Washington, Ben Franklin, and John Adams were all federalists.
Anti-Federalists believed that there should not be one strong central government, since they believed that this was a form of Tyranny. They believed that this would take away states' rights. They wanted the Bill of Rights ratified. Most of them were farmers and tradesmen (less wealthier people). Thomas Jefferson, Patrick Henry, and Samuel Adams were all Anti-Federalists.
You could argue that in the end both got some of what they wanted. The Constitution was passed and a Bill of Right as well .