In both dramas the main heroine changes identity and seduces a man who wronged her as a revenge. Both are a bit campy and over the top.
Supernatural powers, partial memory loss that is related to their accident/murder, killers are also quite similar to eachother. They both have a very similar feel. The guys also appear to have a hard shell but are secretly total cinnamon rolls.
The only similarity is that both dramas are about corrupted schools and bullying and main leads trying to change that. Gakkou no Kaidan is a bit more idealistic I would say.
There are definitely some similarities between these two dramas. In IHYV it's a guy who gains special abilities after an accident and then helps a lawyer, in TGWSS it's a girl who gains special abilities after an accident and then helps a police officer. There is also revenge in both dramas.
Both main guys don't want to get married, but their family is pressuring them, so they pretend to date a girl that their family won't like.