Both movies are romantic comedies with a focus on sensual/sexual topics that are most often not openly taked about. "Love and Leashes" deals with BDSM and the romance plays a subordinate role (pun intended), while "My P.S. Partner" is all about phone sex, satisfying a persons needs and cheating in a romantic relationship. Both are quite funny and surprisingly sexy.
Both movies delve into the world of BDSM and how it may free the people involved. "Love and leashes" gives more of an introduction into the matter for someone with no prior knowledge but "Nana and Kaoru" as well shows one experienced partner and one newbie who discovers this new world. Both movies are ultimately comedies and have a slither of romance in them even though that is not the main focus.
Both stories are located in traditional Japanese sweet stores with a long history. Although both have different genres as "Watashitachi wa Douka Shiteiru" is a murder mystery and "Fukuyado Honpo" is a romantic comedy, they both focus strongly on the traditions involved with Japanese arts and the duty of the younger generations to inherit the long standing businesses and continue the family legacy. In both shows you will see tea ceremonies, beautiful and tasty looking sweets and plenty of people wearing kimonos.
Although one movie is about a zombie virus while the other is about poisonous gas, in both the male and female leads have to find a way to safety and have to fight their way trough appartment/office buildings. In both movies the male lead is on the clumsy and goofy side while the female lead has her shit together.