Vatican Kiseki Chousakan

The style of inquiry and mystery is very much like supernatural in addition to being two people looking at imaginary issues  

Both Vatican Kiseki Chousakan and Ghost Hunt share an atmosphere of highly stylized mystery. There is a sense that the protagonists are trying to rationally examine a supposedly supernatural phenomena through the lenses of Science and History. There are situations that are genuinely horrifying, but there are also moments of extremely campy graphic violence or splatter effects. Fans of one would likely thoroughly enjoy the other. 

Both are campy, but enjoyable, horror mystery shows. Both are also pretty obscure and rely heavily on inspiration from Western horror films.  

The main character, Sherlock, as well as his assistant, Watson, are tasked with investigating murders. Sherlock is tasked with using his wit, knowledge, and skills at finding the culprit to these murders. Conversely, Moriarty is another main character who uses his support to bring judgement down on the corrupted. 

In both series there are detectives trying to solve supernatural mysteries Both series have ''literary'' theme In both shows two main characters are very protective about each other, tall and older one being a little bit more protective (Dazai-Roberto) about younger and short best friend (Atsushi-Hiraga) In both shows we see ''abusing of young children in church'' theme They are both seinen and they have protagonist with dark and troubled past. 

Both bear a similar dark aesthetic/plot and revolve around religious themes. 

Similarities: -Both Anime tell about an organization which is based out of Vatican. -Both have Priests who do the mission. -Both have Dark Atmosphere. (Although Ao no Exorcist still has some comedy moments) Differences: -While Ao no Exorcist focused on battles & how they do the exorcism, Vatican Kiseki Chousakan focused more on religion theme & mysteries. -Vatican Kiseki Chousakan targeting the adult audience, while Ao no Exorcist targeting the younger audience. 

The dark Thriller atmosphere involving Supernatural themes are really similar and I immediately thought of Mouryou no Hako when I finished the first Episode of Vatican Kiseki Chousakan. In Mouryou no Hako we have a group investigating a murder case while in Vatican Kiseki Chousakan they're investigating "miracles" which also involve bizarre and complex events. Both are dialogue heavy series, giving us little hints and leaving us excited after a Episode (my first impression of Vatican). Both MC's are priests and have similar traits in their personality and looks (Robert sometimes acts like Chuuzenji and Hiraga looks like a younger version of him).  

They both have the same mysterious vibe, but it seems the cases will take more episodes to be solved in Vatican Kiseki. Give it a try if you liked Gosick. 

Like Vatican Kiseki Chousakan tactics is also about mystery that has the context of a particular mythology/theology. Unlike the the Vatican cases the mythology/theology is not christianity but has more to do with japanese myths. Also unlike the Vatican show ( so far )Tactics has more of a emphasis on the fantasy and supernatural elements, however the dark mystery vibe is similar between both shows.  

... because Christian imagery and Nazis are exotic or something. Hellsing is heavier on the Nazis and VKC is more focused on Catholic esoterica but plenty of both in each. Both are gratuitously dark, with plenty of death but also plenty of black humour to lighten things up. Hellsing being the gorier of the two. 

Plot twist/escalation extravaganza + highkey homoromantic tension. SamuMenco has one continuous plot whereas Vatican Kiseki Chousakan are separated into (more or less) discrete independent cases. Incredible whiplash inducing pace but since they're fairly divisive shows if you really enjoyed one, give the other a try. 

Both are incredibly memeingful, unintentional B horror-esque comedies that just keep escalating the further in you get. Testing the very concept of how much suspension of disbelief one can have.  

In both series the main characters are solving supernatural mysteries. The tone is quite similar.