One of the main leads in both dramas travel back in time by falling into water, but Go Princess Go puts an extra twist to the concept with it being a guy waking up in a girls body, which kinda adds another dimension to the ensuring love story. However, neither lead seems to be overly concerned to have traveled in time and neither tries to intentionally (yet) change any course of action in history (such as e.g. Faith) while being perceived as a bit weird/too freely spoken by the other characters. Moon Lovers is more visually stunning while Go Princess Go relies on some sassy comedy.
Both dramas incorporate modern elements, Moon Lovers seems to be big on modern themed music while Go Princess Go tries its hand on more visual and modernized outfits & settings.