What conflicts emerged first during the writing of the Constitution and later during the ratification debate? How did the choice of the federal model influence or was influenced by the Madisonian Model, relating to the constitution?

The primary conflicts that surrounded debate on the writing of the Constitution in the summer of 1787 focused on the differing concerns of small and large states. This is best understood by considering the debate over Article I, which is concerned with the legislative branch of government. Larger states (in terms of population) wanted representation in the legislature to be based upon a state's population. Smaller states were concerned that they would be overwhelmed and lose their sovereignty and representative clout under such a system. They felt that each state should be equally represented in the legislature.
The resulting compromise, often referred to as "the Connecticut Compromise" as it was proposed by Roger Sherman of Connecticut, called for a bicameral legislature comprised of two bodies. The first, the House of Representatives, would be comprised of members from each state, and the number of representatives would reflect the state's population. Slaves were defined as three fifths of a person in one of the more infamous pieces of wording in the Constitution. This was done because southern states had large enslaved populations. The second body was called the Senate. In it, each state would have two members. This gave power to and appeased the smaller states. Madison incorporated this compromise in his draft of the Constitution.
During the debate over ratification, it was the larger states that held out the longest. A truly "federal" system or centralized government would not have given as much power to individual states as the US does today.