Shika no Ou: Yuna to Yakusoku no Tabi

The setting in both movies is almost identical, The Deer King is more focused on politics and the scientific approach of the featured plague, while Mononoke has more grand, and impactful impression. 

Moribito and Deer King have a very similar trio of main characters: Balsa and Van are stoic yet thoughtful warriors who only resort to violence when absolutely necessary; they unexpectedly come to care for a dubiously magical child—Chagum and Yuna respectively—and are completely out of their element at first, but come to think of their charge as family; Tanda and Hossal are soft-spoken herbal healers who support each pair on their quest. Additionally, each core trio subverts gender roles—particularly parental expectations—in distinct yet satisfying ways. They also have similar settings and world-building, incorporating elements of both Japanese and European medieval periods, and feature nature-based magic. A small similarity (but one of my favorites) is that both devote a decent portion of their runtime to their characters leading small-town lives in a peaceful village. These sections border on slice-of-life, and make for a nice change of pace in the center of both works. (Both were animated by Production I.G. and are based on novels by Nahoko Uehashi, of course, but the works' similarities run far deeper than their shared origins.)  read more 

Both shows have distinct world building, featuring two factions. In both stories, the main characters are people who had suffered from the internal conflicts, and stoically tries to find the right solution for this conflicted predicament. 

Both animes have a similar setting (pseudo mediaeval) and wolves play a crucial role in both mediums.