Both share many themes. My favourite being that constant question of: To leave or to stay. When the going get's tough, where do you draw the line among those you love and care about the most? In the end the answer is there is no line if you love them because love covers over it all. King's family offers an alternate ending for those Happy Home fans who were dissatisfied although while i enjoyed King's family just as much i'd venture to say the ending is not realistic but many people enjoy that sort of thing.
Cha Soo Hyun's character in encounter is similar to Hae-Ryung's story in Happy Home. They both play unhappy, aloof but dignified daughter in laws with disapproving mother in laws. Both were married into rich family and get divorced by their husbands to let them free. Both ex-husbands love them still and want them back in their life. Even the divorce contract also is similar. Both are lucky to have a new man in their life who love them immensely.
Both shows feature multiple storylines that follow different characters as they navigate love, marriage, and the various difficulties that come with them. In "Goddess of Marriage," the main characters are Hae-Ryung, Man-Ho, Hae-Won, and their family members, who are all dealing with different aspects of love and marriage, such as infidelity, family conflict, and the expectations that come with being a spouse or parent. Similarly, in "Red Balloon," the main characters are Jo Eun Gang, Ji Nam Cheol, Han Ba Da, and Go Cha Won, who are all dealing with their own personal struggles within their relationships. Both shows delve into the emotional struggles and challenges that can arise within personal relationships, and how different characters cope with and navigate these difficulties.