Both are about a man using his supernatural abilities to solve cases. In Cheo yong, it's a detective whereas in Vampire Prosecutor ... well it's obviously a prosecutor. Both are short dramas ( 12 episodes for VP and with a second season).
Both are dealing with a student falling in love with an older guy. In both movies characters are mentally tortured because life isn't going easy with them, but thanks to their beloved they still manage to get through it.