When the Constitution was being debated, the Federalists were in favor of ratifying it while the Anti-Federalists were opposed to its ratification. The reason for this was that the Anti-Federalists were concerned that the proposed Constitution would give too much power to the federal government. They felt that the federal government was too likely to be oppressive just as the English central government had been. Therefore, they wanted a constitution that would be more like the Articles of Confederation had been. They wanted one that would give more power to the states than to the federal government.
So, the two sides disagreed on whether to ratify the Constitution. Their disagreement was caused mainly by a disagreement over how much power the federal government should have.