Makaryuudo Demon Hunter

Both Anime are from the 1980s and are classic Gothic with a female heroine with supernatural powers. 

Both of these series are Gothic horror from the 1980s with classic horror elements, but with a main female protaganist. 

Both are half-hour, one-shot '80s OVAs that feature a group of high school students getting inadvertently involved with the supernatural. "Makaryuudo" is a little more dark and violent, but both shows manage to maintain an overall lighthearted tone. 

Demon and human relations? Who would have thought? Well, the main protagonists of both of these series dive right into the whole mess of demon and human relations, one taking place in a modern setting and the other time traveling, but they both kick butt, or the one from InuYasha does eventually after some character development. The style of the shorter series also reminds me of InuYasha's style. 

Both anime have a main protagonist who fights demons trying to destroy humanity. Both anime have similar demon designs (The bird demons in Makaryuudo Demon Hunter look very similar to Sirene from Devilman). Both are action-packed anime from a similar time period (late 1980's - early 1990's) with violence and blood. However Devilman is way more violent and has more nudity compare to Makaryuudo Demon Hunter. If you like one, you may enjoy the other.