Cop Craft

In both a portal from another world opens up on earth and two races intertwine. In both vampires are mysterious and strong. 

In both shows, a portal opens and connects two diffrend worlds a fantasy and a modern one. The shows involve a millitary/police guy and girl(s) from the fantasy world where they work together fixing problems along the way. 

Mysterious vibes 

The female protagonist doesn't look as if they can do much of anything, but their looks are deceiving. Both series also take place in a future that humanity didn't expect, one where magic is real in some way. Over the course of the series, the main characters who are partner strengthen their bonds. 

The shows feature a main character with similar personalites. They are crude, affected by past war experiences and harbour a dislike of the race of their partners. The stories are similar as they follows the view of two unlikely partners as they fight "crime". They feature a heroine who the main character doesn't initially like but he starts to warm up to them as the series progresses. A different dimension/world is important to both plots.  

He, the main male protagonist, finds themselves stuck with an unusual partner, someone they didn't want the help of along with being dragged into problems unlike the ones they've dealt with before. Then there's the art for both. 

Both of these series follow a newer trend of blending fantasy with detective instead of paranormal with detective while putting their own twists on the blending of genre. There's also the element of the cities being built around fantasy becoming an unexpected reality for those who've never been exposed to it, or perhaps magic becoming reality becoming an unexpected reality. 

While the mixture of detective and paranormal are popular, a mixture of detective and fantasy is less common, yet these two series manage to blend the two. And, of course, the enemies use music, something normal detectives aren't used to when trying to solve a mystery. 

Similarities: 1. The same mystery and action genre. 2. The same one older guy to younger girl kind of partnership. 3. The same situation plot where it involves a bigger villain that the duo has to deal with. Dissimilarities: 1. Different futurist , where one is about mankind dealing with demi-human beast, and the other was mankind dealing with entities from an alternate world. 2. Different female main characters attitude, where in one anime the girl is a kuudere/lesbina/air head, while in the other anime the main female character there was more of tsundere/airhead/bokuko. 3. Different main guy attitude, where in one anime was very analytical but very cautions, while in the other anime the main guy there was very much aggressive, but a bit of a procrastinator.  read more 

Similarites: -Both were classifies as reverse isekai, where other worldly entities travel through the modern world. -Both have the same characters whom were warriors in their own right. Dissimilarities: _ One was more about action, magic and supernatural, while the other is more on action, thriller and sci-fi. 

The same story about detective. In this anime,its about detective that set to revenge his partner death and of course it ends with a bang! 

If you liked the mystery, detective show-esq vibe that good part of Engage Kiss have you will probably like Cop Craft Both have smoking protagonists with a dark and mysterious backstory with a magical girl who uses a sword. but that's just superficial details, the biggest and important thing is the tone. The criminal underbelly of a city that sells itself as a paradise, the crimes commited both by human and mistical beings, etc. Cop Craft has a very similar vibe to Engage Kiss, only with much less romance. 

Same older guy to loli professional, kind of relationship, where the older guy has experience but starts to get stale while loli profession can kick ass really bad.  

both anime about fairies and mythical creatures that are almost extinct, both about investigators protectingthe fairies 

Although in a gritty magical girl setting, the general synopsis is fairly similar. Both worlds suddenly have a mysterious gate that opened up in the human world, bringing in fairies and monsters alike. Humans and supernatural creature begin orchestrating crimes, and there's a force to oppose them etc. 

The same relationship that involves older guy with younger girl, were they have to go to such hardships in order to succeed.  

Buddy Cop mysteries set in basically similar settings