Kawaisugi Crisis

Two comedies centering around animals, both feel quite similar with how they more or less talk about different animals and focus on specific species at times. Differences would be that Tendebu is about the creation of animals and Kawaisugi Crisis is about discovering different cute pets. 

Both anime follow an alien whose organisation aims to wipe out humanity for earth. Both the main characters find an earth animal so irresistibly cute. I would say they have similar humour with Kyuujitsu no Warumono-san being slightly darker. In Kyuujitsu no Warumono-san the main character falls for panda bears. They just want to enjoy their days off and not have to fight the sentai and find panda bears relaxing. Follow his antics as he avoids anything related to work! In Kawaisugi Crisis, the main character falls (at first) for domestic cats. They want to study all the cute animals on earth (even if it kills them!). Follow their antics as they go deep down the cute animal rabbit hole. read more 

Both get their comedy from the simple pleasures in life being ramped up to the extreme, with protagonists being 'tortured' by how good these things are. In Himesama, it's often food being too good. In Kawaisugi Crisis, it's animals being too cute. Comfy and fun, lighthearted watches. 

Absolutely hilarious and funny cat themed comedy anime. I do agree that animation is a bit lacking in this. Although I still find it funny to watch especially for those who have had cats or like cats. 

Friends taking care and raising pets together, also both have comedy aspects.  

A cute alien girl descends to Earth and hilarity ensues due to misunderstandings 

The way main characters (Bocchi and Luna) react to things or situations that are too overwhelming for them is similar. So if you are looking for characters with funny reactions you might check out them both.  

Both anime have a cat that was rescued after being abandoned by owners who did not have the patience to rear a kitten. Both are very wholesome and funny. Both have a clumsy / goofy character. Kawaisugi Crisis follows an alien who has never seen earth animals and adopts a cat to get used to how cute earth animals are. Funny shenanigans ensue. Atarashii Joushi wa Do Tennen follows a man trying to over come his past with a power harassing boss with his new goofy boss and his cat and co-workers. Wholesome and funny shenanigans ensue. 

Both series features many cats and taking care of them. Even though stories themselves are different (cat and normal person versus cat and alien), both are wholesome as they show the cat and owner relationship. Kawaisugi Crisis seems to focus on other animals as well, Doukyonin features on cats mainly. So yes, if you are looking for series with cats, you can check out both.