PriPri Chii-chan!!

They are shows focusing on humans taking care of small creatures, that are meant to be more cute. PriPri Chii-Chan!! is more about the cute and funny situations both the girl and the creatures have, as well as all the different characters with distinct personalities that they meet. "How to keep a Mummy" meanwhile takes a better look at it's group of human characters and creatures. It's a lot more grounded and tries to take a look, at what these creatures would eat/do/what kind of abilities or personalities they have and more. Plus, it does have a little more drama with each of the main human characters. 

Squishy fictional characters living within everyday modern Japan being taken care of by a girl. Both shows are perhaps more girly in nature and targeted more towards children, tho I feel Chii-chan is more for children~teens whereas Punirunes is more for toddlers~children kinda ages. In both shows, characters meet a variety of different characters, Chii-chan has new chiteijin and random folklore characters shown and Punirunes has new punirunes shown, coinciding a happy everyday life of random fun activities, tho Chii-chan is a slight bit more story-based compared to. Perhaps the biggest differences are that in Chii-chan, their extra characters are kept secret whereas Punirunes seems like common knowledge to everyone, also that Chii-chan series derives from a manga serialization whereas Punirunes series derives from the digital interactive toy (similar to Tamagotchi). read more 

Children's shows featuring a girl taking care of cute creatures, tho despite their demographics are children, Chii-chan feels more suitable for children slightly older than if it was for Cocotama. There are characters that are silly and full of everyday fun but creatures in both are kept a secret to most humans whilst the creatures strive in a goal throughout both, Chii-chan repaying kindness to the MC whilst Cocotama are little gods trying to help out everyone in order to become fully fledged gods. The shows are very colourful and there ain't really much threat going on, just the daily lives of the characters as something exciting happens in their everyday lives with the addition of the creatures whilst going to school normally too. They both also have Aki Toyosaki playing as a pink creature and also her doing an ED song as well which is really coincidental. read more 

Silly shows for silly people x) Though Shizuku-chan is set in a fictional world, they share a similarity with fun and joyous everyday activities featuring an array of different crazy characters within the main lot of the group as well as episodic characters but both MCs are pretty dopey and silly as well. These are perfect kids animes for people who just want a good time and love to feel silly like I do xD 

Both series have middle school responsible girls as main character who takes care of small, kawaii beings... and the same author of course.