Damekko Doubutsu

Primarily, both involve animals and have short episode lengths - Chi's Sweet Home with episodes around 2:30 minutes each and Damekko Doubutsu with times around 5:00 minutes in length. They're both sweet and comedic, and both are meant for children. Damekko doesn't have the 'Awww' factor that Chi does, however, but they are both similar in other respects. 

Both are shorts concerning animal like characters of varying species and personalities. Also, both are cute and have little active plot. If you enjoy one, you'll definitely enjoy the other :) 

Fruits Basket and Damekko Doubutsu both have very similar characters. As well they both have animals, but Dameko is different, it's a sterotype of an anime character given to an animal. Just by watching the first few episodes you can see the resemblance between the characters like Ushara is to Kyo and the unicorn to Ayame. Also, the art style and humor is very similar. However Damekko doesn't really have a big plot but instead just the parody of characters. 

Both are short comedy series where the main characters are animals/people in animal costumes 

Both are heavily chibi animated with senseless humor and "useless" characters and that is what gives them their charm. Adorable and funny anime good for anyone. 

Both are about a group of different humanoid animals mingling with each other. Ranka and Uruno are both wolves separated from their pack trying to find their place in the world.  

Both are full of irony and sarcasm 

Nyoro-n Churuya-san and Damekko Doubutsu are both short and very funny. If you like random humour and chibi style of characters, you definitely should watch Damekko Doubutsu. 

These are very similar for character wise. There are lots of cute animals and chibiness. The stories are both very cute.  

It is a very similar comedy atmosphere. You can imagine Guu as Unihiko, Ureno as Hale, and Usahara as Weda.  

Both are extremely short(around 5 minutes?), and very cute. Damekko Doubetsu will have more laughter, but Ocha-ken has a sweet and 'awww' inspiring aspect about it. Both series are about animals; Damekko Doubetsu about useless ones, Ocha-ken about tea dogs (and cats).  

Damekko Doubutsu and Zenryoku Usagi are both kids' anime, with episodes less than ten minutes long. They share many of the same humorous points, too: both have comically useless protagonists who are always getting picked on by more confident (if no less odd) supporting characters, both contain just a tidbit of drama to even out the comedy, and of course, both feature cute animals. Anyone who liked one will probably enjoy the other. 

Both anime are about human personifications (In hetalia its Coutries as humans, in DD its Animals as Humans.) In Both cases All characters are seriously flawed, and the story focuses on their day to day failures in a cute wayxD Both are comedy, are 5 minutes per episode, and make absolutely no sense in an awesome way =D