I’m interested to hear about anime that give a different experience when putting the episodes in a different order. They can be official orders (broadcast vs dvd) or fan orders (moving arcs around, putting seasons in chronological vs release order). Maybe you can even think of examples where a companion movie is inserted in the middle of a season? Two separate projects by the same author or studio that can be weaved together to form a consistent whole?
I think Monogatari series is a classic for this: broadcast vs novel vs chronological. I’d argue Fate as well. Doing Zero before the Stay Night trilogy gives a different vibe to some of the plotlines than after (dramatic irony vs mystery).
Zero was so boring