Both have a peculiar and reclusive older male lead that enters the female leads lives. They help eachother grow and overcome problems. Both shows also tackle inequality, bullying and student life.
They are similar in that they have a teacher and student living together secretly. My little bride they are actually married through an arranged marriage.
They both have cohabitation as a theme, Hotaru no Hikari is about a woman and her boss secretly living together due to various circumstances. They also both have romances develop due to living together and caring for each other.