James M. McPherson's "Battle Cry of Freedom" (Oxford UP, 1988) has an interesting (if somewhat orthogonal passage) on the role of political parties in the Union and Confederacy:
Formal political parties did not exist in the Confederacy. This state of affairs arose from two main causes: the erosion of the two-party system in the 1850s and the perceived need for a unified front during the emergencies of secession and war. Southerners considered this circumstance a source of strength. ...But in fact, as historians now recognize, the absence of parties was actually a source of weakness. In the North the two-party system disciplined and channeled political activity. The Republican party became the means for mobilizing war resources, raising taces, creating a new financial system, initiating emancipation, and enacting conscription. Democrats opposed most of these measures; the existence of this well-defined opposition caused Republicans to close ranks when the chips were down. Because measures were supported or opposed by parties, voters could identify those responsible for them and register their approval or disapproval at the polls by voting a party ticket. Both parties, of course, used their well-oiled machinery to rally voters to their side. In the Confederacy, by contrast, the Davis administration had no such means to mobilize support. No parties meant no institutionalized discipline over congressmen or governors. Davis could not invoke party loyalty and patronage in behalf of his policies, as Lincoln could. Opposition to the Davis administration became personal or factional and therefore difficult to deal with.This implies that the main function of the party system is not to represent coherent ideological positions, but rather to focus support for or opposition to the governing party. And indeed, even aside from Duverger's law, it seems to me that the main distinction between the parties is governing vs. opposition. The two contemporary parties have a governing form and an opposition form that contrast with each other, which helps explains Jane's Law: "The devotees of the party in power are smug and arrogant. The devotees of the party out of power are insane."
In the North, where nearly all state governors were Republicans, the ties of party bound them to the war effort. In the South the obstructionist activities of several governors hindered the centralized war effort because the centrifugal tendencies of state's rights were not restrained by the centripetal force of party. The Confederate Constitution limited the president to a single six-year term, so Davis had little reason to create a party organization for re-election. Such government policies as conscription, impressment, the tax in kind, and management of finances were the main issues in the congressional elections of 1863. Opposition candidates ran on an individual rather than a party basis, and the government could not muster political artillery to shoot at all these scattered targets. (689-690)
Following the Civil War, the Republican Party was the leading governing party in the North (while the Democratic Party was the main opposition party there), while the Democratic Party was the leading governing party in the South (while the Republican Party was the main opposition party there. The Democratic Party was a famously Southern agent of Jim Crow and white supremacism until the 1960s. But as for the contemporary parties, it's almost as if the old governing-party form of each withered away and disappeared, leaving the opposition-party form as the new governing party in each section. For whatever sectionalism remains, the Democratic Party has become the leading governing party in the northeastern United States, while the Republican Party has become the leading governing party in the southeastern United States.