The series were actually independent of each other, unlike Beverly Cleary's series with Henry Huggins and Beezus and Ramona overlapping. Nevertheless, they were both entertaining. Both kids get themselves into precarious situations and have to find their way out again.
Eddie was notorious for having way too many animals. Little Eddie is the first book in the series, that introduces us to him, his siblings and all of his animals. In Eddie's Menagerie, he has to care for a bunch of animals as a part of his job in a pet shop. In Eddie and Louella, his beloved pet parrot is accidentally misplaced when he loans her out for a charity function. In Eddie and the Fire Engine, he gets a pet goat. And in Eddie Makes Music, he learns how to play musical instruments.
Unfortunately, for some reason, Eddie's books are all out of print at the moment. Your best bet is to find them at a local library or used bookstore. I am fortunate enough to have collected some from an antique store several years ago. They sit on a shelf alongside some of my books about Betsy.
Carolyn Haywood's books about Betsy are still available for purchasing, as they have never gone out of print. B is for Betsy is about her conquering her fears about going to school in first grade. Betsy and Billy chronicles her adventures in the second grade, including losing teeth and getting into trouble with her best friend Billy. Back to School with Betsy shares her disappointment in losing her favorite teacher in third grade. Betsy and the Boys is about her wanting to play football with the boys, who of course don't want to play with a girl. Snowbound with Betsy chronicles her family being stranded at home during a blizzard. Betsy's Little Star is about the birth of her baby sister. There are even more adventures about Betsy, as well as a few other series by Carolyn Haywood. She wrote over 40 children's books.
All of these books are wholesome and entertaining to read. They were written during a more innocent time in children's literature. It's too bad that there aren't more books like these being written today.