It is clear to me that the Fae Houses mirror each other: Vengeance to Valor, Pride to Ballads, and Seasons to Sorrows. It is unclear, though, just what the relationship is.
While Vengeance seems to encapsulate anger and rage, Valor is a more structured focus on combat - learning to fight instead of restraining an incessant berserker rage. While Valor revels in combat, Vengeance doesn't have that luxury and features stoicism and determination "that [makes] granite seem soft and fickle." Interestingly, both of these youngest Houses were taken over by forces that proved better than the Fae at what the House represented: Valor by Hroth Magnus, a mortal who mastered combat better than the Fae could in their cycles; and Vengeance by Tirnoch, whose rage and desire for vengeance against those who imprisoned her knew no bounds.
Pride and Ballads appear to be the most perfect mirrors here, each celebrating its respective Court's greatest heroes; I, for one, believe that Magwyr is in the House of Pride. But in an interesting reversal, Pride's secretive, backstabbing nature is well-known (it's mentioned by Alyn Shir as a given, for example), while the fact that the House of Ballads retells tales with different actors is closely-guarded knowledge and Hallam the White frequently works without other members' knowledge (such as on the Fae Cairns). Such secrecy is not commonly held as a virtue among the Summer Fae, though it could be, judging from their common folk and how Wencen speaks of Hallam's doings, that the Summer Fae are simply more willing to embrace a simpler outlook on life that does not allow for such complex activities and secrecy, assuming trust and openness rather than needing to pay close attention to everything for fear of betrayal.
We know very little about Seasons, though it has a clear emphasis on wisdom and an understanding of the Cycle that connects readily to Sorrows' death-focus. Amusingly, they're also connected by their utter lack of membership at the time of Tirnoch's fall, though this is also relevant symbolically as the Courts' wisdom and identities are the first things consumed by Tirnoch's madness. It's possible that Nyralim serves as a foil for the Gallows Tree, with Nyralim actively providing wisdom while the Gallows Tree carries death. (Both Nyralim and the Gallows Tree are also more adopted by the Fae than actually Fae in nature.)
With each an inversion of the other, could it be argued that each House represents one of that Court's major virtues? Pride, Vengeance, Seasons (as wisdom and understanding of the Cycle), and Valor easily fit into this pattern, while Sorrows is a stranger fit because it's less a virtue and more a fact of the Winter Fae nature which must be simultaneously rejected and embraced and Ballads is quite difficult to include because the closest virtue is one of unity rather than about the stories themselves. When the House of Ballads is discussed and explained by Summer Fae, it is described as providing a common narrative that links their kind together and provides stability, though this understanding pushes it towards being a foil for Sorrows instead of Pride as a means for building up and supporting the Court. The inversion, then, comes about through one Court's virtue being the other Court's sin.
Feel free to comment, criticize, question, or propose alternatives in the comments section!