Both are long family dramas with approximately the same runtime. Person Who Gives Happiness is 118 eps 30 minutes each. Come Jang Bo Ri is 52 eps 60 minutes each. Both female leads adopt and raise a child. Both female leads find sweet husbands that help them to deal with the evil schemes of others. Sweet romances with lots of makjang drama.
Both series have birth mothers who are bad to their child, leading another woman to start caring for the child. However, the birth mothers stay in the picture and complicate the situation. Though the premise is similar, Mother is a lot darker and sometimes harder to watch. It includes physical child abuse, while Person Who Gives Happiness leans more towards child neglect/emotional abuse. Both shows will make you emotional as you watch. Person Who Gives Happiness is a longer drama, but well worth it if you stick to it. Mother is much shorter, but packs a lot into its few episodes.
In both these dramas, the main character adopts a child and does her best to protect and raise him. The main characters are betrayed by the men in their lives, but they meet someone new that loves them and their adopted child. The adopted child's birth families are terrible awful people in both dramas. The main character has to fight for custody with the birth families.