Kirari remarks that Rei acted as the Joker in the election, as Terano remarks that Yumeko fulfilled the same. I don't need to bore you with the composition of a playing card deck and draw out the entire metaphor, but I will make this clear - the first series was a far more theoretical work, based on introducing and demonstrating mechanisms of power as Yumeko set them to work, demonstrating via stress. The second series is a more traditional series, about the process of power being born from competition & chaos.
Yumeko acted as a scourge against the machines of order the Student Council had constructed in the last game, finally finding her equal Magician with the blood red of her own eyes met the pale lunar blue of the president's. In this series, the story is about hierarchy - its origins and construction.
The arc of the series is the actions of hierarchy, through several lessons. The student council games questions the questions asked of a hierarchy, Yumeko working through them as our eyes into the series. The Batsubami arc is of how the lesser becomes the superior by rejecting the chains that bind them. For that, some would question how she broke her chains so thoroughly and to them I remind them of an anecdote during the sinking of the Titanic, where the third class passengers, even as many had some hint of a chance to break to the upper decks and attempt to survive, huddled in the common rooms, reciting prayers and looking to the sky, begging, like their ancestors had for millennia in feudal Europe's caste system, for their superiors to determine everything for them. The Batsubami arc was of new powers being born as the inferior realized something of their own, rising above to become a full human, with a name - beyond the animal existence of livestock. Finally, the romantic arc between Kirari and Sayaka speaks of the purpose of a true inferior. Sayaka operates wholly on logic, the blunt instrument of the physical world. She and Kirari sink into death's infinity together and emerge wedding - Kirari as Heaven and Sayaka as Earth in a beautiful romance that makes allegorical argument for the existence of caste.
While not as good as the original, for simple reason of being more specific and less abstractly broad-reaching, it's still equally worth watching if you learned anything from the first. My only mark of shame against it is that we don't see more with Yuriko and Midari - Fate and Violence respectively, their wedding could make a truly powerful work in the same fashion as Sayaka and Kirari!