Both dramas have bold FLs protecting the balance between the demons and the human world, and reserved but devoted MLs who are officials. The ML in You Have My Heart was also in Moonlit Reunion.
Human ML's and both FL's a powerful non-human spirit lords that appear cold and unloving in the beginning but warm up to ML, protecting him from their magical world.
Both FLs are powerful and non human, bound to protect a certain place, and the MLs are humans whose job is solving crimes in the adjoining village. Both leads have a past life connection.
If you are looking for something shorter, this has very similar dynamic, much like Love Beyond the Grave, FL is a powerful demon, who appears cold and mean and ML is a a very clever scholar.
K-Drama 
