Kamisama Kazoku

Both these series contain the "goddess" theme, becoming one of the major themes. There is envy, jealousy, and later love present in both series as the episodes progresses. Both series contain supernatural elements as well as mixed in comedy and misunderstandings. Also, expect drama and the "little sister" annoyance that are present who tries to help the main protagonist through his problems. (namely involving love)  

In both, the protagonist is a powerful heir of a supernatural (god/demon) family but tries to live as an average human, causing funny situations. Both also have a romantic storyline. 

The fact that there are gods and that it shows the abilities they may have. 

you see,the title has the kamisama which both anime also have gods in fact, kamisama hajimemashita is about fox demon protecting the girl, but the angel watches over the god in kamisama kazoku:3  

The main heroines Taiga and Tenko in both are Tsunderes who want the heroes Ryuji and Samatarou to fall in love with other girls Minori and Kumiko but end up falling and pairing with them themselves. 

there is an angel in both of this animes,their drawing are similar and they have the similar atmosphere:) 

It about God and angel :D I like it though :) It similier about angel and the mains fall in love <3 

Shuffle is also about Gods and Demons going to earth and experiencing the life of being human and falling in love with a human. n_n 

Besides both being Comedy-Romace animes. They both have a sci-fi like aspect to them; but the opposite way than the other. But, if you like one I'm sure you'll like the other. 

Both deal with "odd" families that have something to do with gods/demons. Kamisama Kazoku focuses more on romance while Kyouran Kazoku Nikki focuses more on randomness. 

Despite the lack of superficial similarities in the plot or setting, these two shows are both light hearted and enjoyable romantic comedies. For people who enjoyed Mamoru-kun and are looking for another slightly overlooked, fun romantic comedy, I think Kamisama Kazoku fits the bill perfectly. 

Kamisama is gods living among humans and Kaibutsu is vampires/werewolves living among humans, but both have great characters and hilarious moments.