Yozakura Quartet

The demon-y aspect and supernatural feel to it are very similar. Multiple characters as well seem like they will add to a very Yozakura feel (especially that one dude with the scarf lol). 

The animation is similar, the characterdesign is similar and in both animes the protagonist/s are fighting against creatures who look like humans and have special abilities. 

Both feature similarities between Japanese belief about gods and demons, but mainly demons. As InuxBoku SS includes protecting in a servant/master relationship Yozakura Quartet on the other hand only includes protection of their city. Both have very unique characters that are disguised as human but are in reality another form of demon. I would recommend both animes are good, even though the Yozakura Quartet doesn't make much sense. 

This is a remake that follows the manga unlike the old series. 

Both have similar genre's where there are two worlds one with demons and one with humans. Main female leads has extraordinary powers. Both shows are confusing and don't make sense and may take a rewatch to understand them both. 

Both are shonen series with crazy magic fights, badass heroines, huge trees and the end of the world at stake. 

People, youkai and animals all living together inside a barrier. The protagonists handle incidents that occur in their respective town/world. 

Though petopeto-san lacks battles and superpowers and focuses more on the slice-of-life/comedy part, both anime deal with the issue of the coexistence between human and youkai and the effort to find a way so they can coexist peacefully.  

Haruhi retains the supernatural aspects, centering around a group of 5 instead of 4. While the show's plotines and such differ, the main supernatural aspect of abnormal beings with powers, working to defend either a town, or in Haruhi's case, the earth. Both series also contain a good deal of off-and-on comedy. Plus, Hime's personality sometimes reminds me of Haruhi's. 

Both anime are set in alternative version of present day world. Unlike in reality, supernatural beings are common in both titles. In Yozakura Quartet we have a city that is a refuge for youkai, in Polyphonica a city when humans and spirits live together. Both also have similar theme of office dealing with the supernatural denizens of the cities as the main theme.  

If you like the supernatural/magical element in this series, you would like Rental Magica. It has similar characters: a group of heros with special abilities, in this case an organization, looking to ward off evil in their city. Both have a hint of comedy, darkness, and adventure. Both have very similar main characters: a seemingly normal main guy with a special ability and a strong female at his side. 

they both have guys that are trying to work with the special girls to save their town/city, both the guys have their hands full protecting both the girl and the town, and in both stories the characters have special abilities they use 

Both shows include a human boy who lives in a place alongside lots of youkai, and tend to be fairly random with their storylines. R+V is more ecchi and comedic in nature than Yozakura Quartet, but the latter has better animation and sound than R+V. 

Both shows deal with gods, the supernatural, and are most light fantasies with lots of humor. Yozakura Quartet also has action and battles, while Kannagi has more school life drama; but neither show takes itself to seriously. They are both fairly short (12 and 13 eps). Yozakura Quartet's plot is centered around the protection of a town that is normal, except that it is a haven for beings with supernatural powers who want to live in peace with humans. Kannagi is about Nagi, a self proclaimed kami who took the form of a girl when her sacred tree was carved by Jin, a very normal boy with an absentee father so not parents will question when Nagi decides to stay. Both anime are very cute without being too cute, and the drama, humor, and action keep them from being boring or too typical. read more