Niehime to Kemono no Ou

Both anime begin with a girl stripped of her rights and in chains. Both protagonists have traumatic pasts and don't really care whether they live or die at first. Both protagonists are taken in by powerful beast gentlemen with strong magic and become much happier for it. Both girls fully dedicate themselves to their "savior" beasts as well. While both anime go pretty different directions with their plots, I would say if you like one, then definitely check out the other. 

While the deuteragonists of Somali and the Forest Spirit share more of a parent and child relationship, compared to the romantic relationship of the characters in Sacrificial Princes, the shows share the fact that a young girl is being protected by a "monster" in a land full of beasts who despise humans, and would just as soon kill them on site. Both shows reveal a past where humans and beasts had a falling out and the beasts became the dominant species. 

Both feature a princess in a castle setting with non-human captors, where both princesses slowly realise their monster captors are nicer than they initially expected. Both primarily focus on the human monster interactions. 

Both series feature the princess sacrificing herself in exchange for the greater good. 

Animes with anthropomorphic animals, but also they both touches topics like the unfair status quo and prejudgment between species 

Main motive of both anime is marrying non-human lord of "hostile" kingdom by abandoned girl that tries her best to be great, reliable beloved. Also both main characters are very determined and make bold decisions to reach their goal. 

Fantasy-romance anime with drama that star optimistic protagonists, slightly cold and prickly male leads, and contain themes of prejudice and oppression. 

Both are fantasy stories who have similar vibes and politics, also Yona and Sariphi are strong and smart protagonists that i think everyone can love 

Both feature human and furry relationship, Marbas and Leonhart both love & protect the heroines. They share some sweet and light hearted moments, and of course some drama to accompany their adventures.  

While Sacrificial Princess and the King of Beasts is a bit deeper, An Archdemon's Dilemma: How to Love Your Elf Bride is still sprinkled with similar themes! A powerful ML falls in love with a gentle FL who changes their worldview. Both touch of racisms/classism in their own way. Both have magical elements. 

Both stories center around a main character who lived a tragic life as a peasant in the slums. Nobody cared for her, and she was sold to the king as a sacrifice. However, she was spared and became a princess of the kingdom. There are many attractive anime men, and the main character must learn to become a fitting princess if she wants to survive. 

Both anime are a romance between royalty and a "commoner". In both anime there are strong women who have to prove their worth and overcome obstacles of people who oppose the engagement of the two leads. 

Two 2-season cour romance fantasy animes with a human girl MC and a male MC who's another being, males in both are of the highest authority in their setting too. There is serious stuff happening in both with light hearted moments mixed in as well in their fantasy settings and both female MCs go through a lot of hardships and trials overcoming obstacles thrown their way. The main difference is that Kakuriyo has supernatural beings that have more human-like properties whereas Niehime is mainly full of anthropomorphic characters but with some supernatural aspects too. 

Both about main character is a girl who is to marry a king. The kings are both seem as evil, cold monsters but in actuality, the king is a kind hearted, misunderstood, lonely man. The girls in both series develops feelings and protects the man as nobody protects them. Lots of romance, cute shoujo 

Two fantasy romances with supernatural traits in them and MC girls who think they don't deserve happiness at all but are taken in by someone who gives them happiness. They both contain light-hearted moments amidst the serious drama in their plots/settings and the couples go through obstacles to get to happiness. Main difference is that Niehime has humans and anthropomorphic characters in plus has more combat/violence in its more action scenes. 

Though they have very different settings, both feature a female protagonist who is incessantly cheerful and optimistic despite circumstances that would have destroyed many of us.