Both of these Japanese dramas had elements of:
-Necessary "evil"
-Academic/school setting
-The MC has many secrets
-MC is trying to change the people around him
-They will both keep you guessing until the end
I felt the same vibe from both of these dramas, however, Mr.Hiirajis Classroom has a darker tone than Kazoku Game.

Both revolve around crime and justice, and neither focuses on romance. Both dramas contain a character(s) with a mysterious backstory. The big and obvious difference is the supernatural element brought on by "Vampire Prosecutor."