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In a land overrun by yoma - monsters that feed upon human innards and take on the appearance and memories of their victims - humans are little more than cattle awaiting slaughter. The only opposition to the yoma is The Organization, a group led by a council of mysterious men who send out their all-female warriors (known as claymores) to do their bidding. However, The Organization is not charitable; a town must pay an exorbitant fee for their services. Likewise, many of the claymores care little for those who they protect. Clare, the lowest ranked claymore, lives only so that she may one day avenge her mentor.
Kagome was just a normal girl, until one day she fell into a well that brought her to feudal-era Japan. After encountering hordes of demons and discovering that she's the reincarnation of a priestess, Kagome must now journey to protect a sacred jewel from evil with the help of a half-demon named Inuyasha. Along the way they make many enemies and friends, and travel between the modern and feudal eras.
Both the villains in InuYasha and Claymore are demons and both of the main characters are half bloods that have to deal with the consequences and what that implies for everyone around them. They each have a special sword with which they use to kill the demons. Kagome keeps InuYasha in check not only for his personality but also for his full demon behavior whereas Claire is kept in check by Raki. They have to try and stay in control of their human selves.
As odd as it may sound the Sura creatures from Kubera reminded me of the awakened beings from Claymore. Both are monsters that can take human from, but also have a form that doesn't look human at all. They appear intelligent, but can revert to acting based on emotions, instincts and desires way too easily. Both show little respect towards human life and even their own kin (though there are exceptions in Kubera). If you found those creatures interesting in one series, you might want to give the other one a try.
Note: Claymore features gore, but Kubera does not.
Claymore and Shikabane Hime are about strong females that have unique abilities. While being not quite human that female protagonists have to help their male counterparts, while the series takes you through their unique relationships together.
I couldn't help but think of Claymore while reading Superior. Yeah it's pretty much gut feel. The only obvious similarity between them, is the fact that both of those are medieval fantasy manga (though I'm sure there are plenty not so obvious similarities). Nonetheless, if you liked one of those two manga then you should definitely give the other one a try.
Both Claymore and The Legend of Maian feature a weak boy traveling with a strong, older chick. Also, both of those have this medievalish fantasy setting. If you liked one of them, you might actually like the other one too.