Both series have the main characters chase evil spirits and have special powers to achieve so, besides both main characters being orphans.

Both tackle the situation of a famous lawyer that is forced to take a leave from their jobs after a case doesn't go the way they expected. They both end up being professors too while trying to get their positions back.

I would say rather than similar, they contrast quite a lot. While Moon Lovers has a darker and more complicated plot, Love in the Moonlight is just what you would like to watch after crying because of Episode 20 of Moon Lovers. It will make you smile because of the cute love story, though of course, you will also cry.