Who doesn't love both shows ? A person who don't know what the difference between the sun and the moon, right so first thing first is
Homer Simpson vs Peter Griffin
Both Homer and Peter are alcoholic, over weight and basically dump (not smart at all). They are loyal to their respective families, both have at least one black friend and in one of the cross over episode the simpsons and family guy, Homer Simpson replaced Ernie the chicken and fought Peter Griffin all around their environment.
Both are a loving mother who just want their respective children to achieve their potentials, Lois and Marge both love their husbands so much that see past their flaws and continue to stay with them after their trials and tribulations. Both are unemployed and have numerous jobs ranging from all employment and finally both love their third child (Stewie and Maggie)
Lisa vs Meg
Both girls are socially awkward and fail to find a guy who don't see them as nerds, Lisa excell in playing the saxophone and Springfield Elementary School only straight A student while Meg don't excell in anything at all and is a disappointment to her father Peter.
Brian vs Santa's Little Helper
Both are dogs and belong to their respective families, while Santa's Little Helper can't talk Brian can talk, walk and drive. Both dogs are best friends to Stewie and Bart, but Stewie respect Brian more than Bart respect Santa's Little Helper.
Maggie vs Stewie
Both babies are intelligent and have secret abilities, for example Maggie use her wits to stand out from other babies and can stand up against adults. While Stewie secretly want to rule the world, he is super smart who built a time machine and have a strong love for weapons. Both babies crave for their mother love this is seen on numerous occasions.
Stewie vs Bart
Both are the black sheep of their respective families, they pull number of pranks on those they come into contact with. They have loyal dogs to call a friend and have a passion for being badasses.