Both are historical Korean dramas that have beautiful cinemaphotography and tell a tale of star-crossed lovers. Both also deal with underlining supernatural themes.
Want to know where such a cute story came from? Hana Yori Dango is the original live action adaptation of the manga written by Kamio Yoko. It may be slightly older, but this Japanese predecessor has everything you loved about the Korean version, mixed in with it's own charm.
Kimi wa Petto is the Japanese drama that the film is based upon. It is ALMOST the same storyline but with much more detail and a little more heart.
Both involve curses of vengeful spirits, while one is Japanese and one is Korean they both have really good plots that will make you think twice about pissing off a ghost girl.