The Midrash Rabbah (Shir HaShirim 7:2) equates Shavuos and Shemini Atzeres, calling them both Atzeres (shel Pesach/Sukkos), saying that really Shemini Atzeres should come later on in the year (similar to Shavuos), it is just that the inclement weather doesn't allow for it, see there.
Ramban too draws a comparison, terming the days from Pesach through Shavuos as chol hamoed (Vayikrah 23:36).
Pesach, Shavuos and Sukkos all share in the same basic korban format (Sukkos has certain additions), whereas Rosh Hashanah, Yom Kippur and Shemini Atzeres have a different set (Bamidbar 28-29).
My question is that if Shavuos and Shemini Atzeres are essentially the same holiday then why don't they share in the same korban protocol?