I don't think Westphalia is a useful fixture on which to turn the "governance" (nature?) of warfare; that is, although it ushered in the start of a new political era regarding the characteristics of political states, I do not see the immediate connection to how it changed warfare. Prior to the peace, states maintained uniformed armies and delivered declarations of war; and after the peace, there were still "ungoverned" conflicts. The sophistication in states' ability to mobilize men and material, creating larger armies, had a more clear impact on the conduct of warfare. It's only recent through the proliferation of technology have non-state actors caught up so-to-speak with states in the ability to deliver violence.

If war is an extension of politics, then a change in the nature of politics would change the nature of warfare. Depending upon your selection of political theory, Westphalia did not necessarily change the nature of politics insofar as it was limited to changing how politics was conducted.