Oooku

Both series take place in historical palaces "inner chambers." Some of the differences are that oooku is a male harem instead of women and eunuchs, and that apothecary diaries involves more mystery solving.  

Both are historical and have the same setup of a harem palace 

-Both in the historical japanese setting. -Both are tragedy and romance that have different protagonist for each arc. -The man/woman have to obey the imperial orders regardless of their will -There are concubine roles in the palace and shogun/emperor -Have mentioned of Murasaki Shikibu literature work references. -Have Yuki kaji as Voice actor in both anime. -Similar vibe to it 

Both are set in Edo period in a heavily historical setting. This anime does draw inspiration from the tales of Hikaru Genji, who is the main portrayal of Genji Monogatari. Both anime follows somewhat poetic storyline, very common in stories of the Edo period. The culture of the time period is the main setting behind both anime.  

Historical anime with a major focus on politics, drama, and tragedy. 

Josei period dramas dealing with growing up, navigating relationships, and making difficult, life-altering decisions. Characters are sometimes morally ambiguous, haunted by their mistakes, or asked to come to terms with carrying the burdens of their forebears. If you love elegant artwork and gritty emotions you will probably enjoy both series. 

My recommendation purely comes from the relationship aspects of the series. I couldn't help when watching Ooku realize that Tokugawa Iemitsu's relationship(s) with her concubines, was very similar to that of Akito and the Zodiac. Of particular interest would be Akito/Iemitsu parallels with Shigure/Arikoto.  

Both have engaging political plots and strong characters. Both take place in a fantastical feudal japan with an interesting and consistent universe. Both share a pretty classic art direction and animation, but good enough for the job. 

If you watched Legend of the Galactic Heroes expecting some great political drama and were disappointed, I recommend Oooku. In Oooku, you get protagonists of different ages, genders and backgrounds responding to a catastrophe in their own ways. In that situation, the decisions of the characters and their interactions affect the political and social landscape of a nation. I found it a fascinating watch. However, for an entertaining series of battles involving two young men with seemingly superhuman abilities, go for Legend of the Galactic Heroes. Somewhat shallower than I expected from all the praise, but still good to watch. 

Both series take place during the Edo period but take very slight liberties in how that period actually played out.