In Berachos 51b (8:1), Beis Shammai and Beis Hillel argue about when making kiddush on an ordinary seudah whether one should make the brachah on the day first, or the brachah on the wine. Beis Shammai holds the former; Beis Hillel holds the latter.
In Pesachim 114a (10:2) they have exactly the same argument regarding Kadeish at the Seder. Why do they need to have the same argument twice? Why can't they argue about seudos in general, and I would understand that they hold the same regarding the Seder? Why would I think it would be different?
In fact, the Gemara in neither sugya addresses the replication, but it does explain the argument, and it gives the same explanation. That is, according to Beis Shammai, the blessing on the day comes first because the day is what causes the wine to be drunk, and chronologically the day begins before the wine is drunk. According to Beis Hillel, the blessing on the wine comes first because the wine is what sanctifies the day, and the birchas hayayin happens more often than the birchas hayom; thus, tadir v'she'eino tadir tadir kodem.
Do these reasons not apply to the Seder that we would think either Beis Shamai or Beis Hillel would hold differently?