Sci-Fi Harry

Both series involve people who have special abilities with their minds. 

Psychological conspiracy mysteries for mature audiences. Both leap into investigations of murder and experimentation pertinent to advancing the plot and understanding the story. Police are involved throughout. Indecisive male leads. Mildly similar art. 

Supernatural elements, major characters spend much of the show struggling to solve mysteries 

It's freaky weird. The main character is a wimp who becomes involved in more than his own little world. There is a series of strange murders.  

explores relationships between normal people and those with powers conspiracy and hidden organization 

super-powered humans and normal ones in conflict 

Both have similar pacing, "funky" atypical art, made for maturer audience, misterious persons and organisations, undertone of thriller and superpower thematics. Sci-fi Harry is less fantasy, Gilgamesh more gothic. 

These titles have some points in common. - A physically weak protagonist with strong psychic powers, which can affect physical objects. - Many spoons are bent. - There is a persistent ghost. - There are fake psychics. - And artificially produced psychics. - The artificial psychics were produced by a secret organization, who wants to use artificial and natural psychics for its own purposes. - The secret organization wants to use the protagonist, thus getting in conflict with him and his buddies. 

Its incredibly difficult to explain this without giving spoilers. It does some very good jobs of torturing its characters in such a varied way that it makes those characters great. The develops of protagonist , and his fear is really believable. The story is cool, although the last episode leaves a little to be desired. You may have heard the ending is unclear. Deep mining in the story and mystery. 

Both of these anime are distant from more common japanese etnocentrism - meaning they are set in America and have zero to none japanese characters, except for that, both are relatively mature mystery shows and in both main character/s realise that they are different than other people and show how they deal with it but also how it changes their relations with other people. If you liked either one of these shows you will most likely enjoy other. 

science fiction and superpowers concerns relationships between normal people and those with powers 

Both shows have young people learning to deal with being super-powered. Both have violent death in them. They have a similarly grim outlook on humanity.  

explores relationships between normal people and those with superpowers in a roughly present day setting 

superpowers and telekinetic mutilation, science fiction in a present day setting, conspiracy and secret research facilities 

supernatural powers characters who don't understand their suddenly weird world trying to learn its secrets gory death 

Both anime have a similar vibe and a similar dark sci-fi tone. The main protagonist in both anime have psychic abilities and uses those abilities to kill people. They both feature a secret organization that wants to use their power for evil. If you like one, you will enjoy the other.  

Well even throught the other is a movie and the other a tv series they are pretty damn simmilar similarities 1) they are all about pshyicic power that the character have. 2) the charaters both are the most powerfull pshycics and both just realising there powers 3) both are being chased by the govenment. in Akira its the other way around Disimilarities 1)In Sci-fi harry the main character in the phsycic user where as in Akira its the second main character. 2)Harry in Sci fi harry is not neccesarily Evil but Testuo from akira is.  

Both create a similarly disturbing mood. Both have awkward social interactions between major characters. Both have a present day science fiction bent.  

Some characters are not as human as they appear to be. Major characters spend the whole show trying to learn what is really going on.  

Several characters spend the whole show trying to solve a big mystery 

The tone is grim. The main characters find out they have superpowers. They become embroiled in plots and hidden politics among forces they never dreamed existed.  

Some characters are not as human as they appear to be. Major characters spend the whole show trying to learn what is really going on.  

Several characters spend the whole show trying to solve mysteries in a world filled with conspiracy.