The differences between the two major rabbinic schools of the First Century CE, Bet Hillel and Bet Shammai, erupt on this page. Hillel rulings are generally more accommodating, while Shammai are more restrictive. This is why Hille rulings are usually the ones accepted as final.
However, there is some argument that a controversy on this page may have the two schools reversing their usual roles. This produces such consternation that the assumption is they are mis-ascribed!
One discussion, however, is about the order of the Havdalah prayers, when incorporated with the grace after meals. Shammai’s order makes the whole thing longer. But, they have a reason:
Beth Shammai holds that the entrance of a [holy] day is different from its exit. At its entrance, the earlier we can make it, the better. But at its exit, the longer we can defer it the better - so that it should not seem to be a burden on us.
Who doesn’t want to make a holiday last longer! More Shabbat, anyone?