Heike Monogatari

Both eras in historical Japan and very similar to each other and both are realistic but they've some Japanese myths. 

Historical story, unique art style 

Similar time period and themes, distinct art style, but even though it can be a bit overly indulgent and heavy-handed with it's messaging at times (common with a few Takahata works) it's a far better example than Heike Monogatari of a historical anime. 

Inu-Ou shows a bit of the history of the Heike clan in a performative way, the history of this clan is shown in the anime: Heike Monogatari, that shows the history in its happening as if the events were in the present. Watching Heike Monogatari is excellent to know more about the narrated events. One work complements the other. Both show certain spiritual/magical elements/special abilities. Also biwa is an instrument of great importance to tell the story of that time in Japan and the anime Heike Monogatari have a very beautiful Aesthetically work, having several beautiful scenes and landscapes, with attention to small details, as well as Inu-Ou. read more 

The script of Inu-Ou developed in parallel with Heike Monogatari (2022) by the same author (Furukawa Hideo), and shares many story elements. The TV anime shows the fall of the house of Heike, the movie takes place 100 years after it and shows how the story had become an important foundation of Japanese literature and poetry. It covers many historical events seen in the TV showin their larger than life artistic version, as developing mythology and supernatural legend. Finally, Biwa music is key in both versions, as both protagonists are musicians playing that instrument. Both were made by two star directors for the same studio. 

Both shows are set in the Heian period (795-1185), before the begin of the Japanese middle ages. Genji Monogatari before ~1000 CE, Heike Monogatari ~1185 CE. The rivaling Genji (aka Minamoto clan) and Heike (aka Taira clan) dynasties were controlling most of Japan during this era. The stories are different (romance in Genji vs. historic drama in Heike), but the period piece elements cover a similar archaic society from the viewpoint of high nobility. Genji focuses on the life of a single feudal lord, where Heike covers multiple. Common plot elements are family life, concubines, love affairs, marriage, societal roles of men and women etc. They feel alien today, e.g. harems were common still. read more 

The main similarity between the two is the setting of pre-modern Japan. Both are inspired by real major historical Japanese events and feature actual Japanese historical figures, while at the same time to the best of my knowledge maintain a good degree of historicity (with the minor embellishments here and there of course). Both also feature more drama than action, despite having two of perhaps the most important wars of Medieval Japan as their backdrop. I strongly recommend both for anyone who likes historical Japanese works of fiction.