Lord El-Melloi II Sei no Jikenbo: Rail Zeppelin Grace Note - Hakamori to Neko to Majutsushi

Both series incorporate historically-based settings and clothing, although Moriarty is actually set in a historical period whereas El-Melloi II isn't. The plot of both revolve around upper class characters solving mysteries and both of the main characters are occupationally teachers who uptook "unofficial" nobility positions. 

Both series feature England as its main setting and display gothic style buildings. Both incorporate wealthy main characters. Both revolve around mystery solving. Both series feature a gothic loli. Both share similar historically based aesthetics via clothing and setting.