Mushi-Uta

Both are very similar but different too. Some of the characters share same roles and strange creatures/monsters play a big part too. Both look sort of the same in style (but Mushi-Uta looks much nicer). One big thing is that Mushi-Uta is way better anime and Ayakashi is very gory. 

Yes, both of these stories are extremely different. They have completely different plot lines but they share an underlying similarity. The most obvious would be the presence of creatures that the main characters are able to summon, and do battle with. The cost of defeat comes at a high cost in both series, and because of this much drama and tragedy ensues. 

It's realy two things of one type. First of all, Mushi-Uta and 11Eyes have similar main characters. 11Eyes like Mushi-Uta is realy cool (and quite strong) drama. but it's spoiler, so i realy don't wanna to tell you about that :D  

Both have the same director, both have odd and off-kilter senses of humor, both have a character who is trying way too hard to be cool, both have dramatic scenes at aquariums, both involve a giant insect that devours people whole. (The centipede in Mushiuta, Sunrise in love live) 

Both deal with competing organizations where one side is trying to exterminate a perceived threat, and the other is trying to help/control their powers and live a 'normal' life. Concepts of worth, rejection, loneliness, mental scars, monster vs human, etc. 

Both anime involve characters who summon dolls/creatures to help them in battles. A character in both shows escapes from a place in which they were being held, which causes many people to pursue them. Also, in both shows, the events of the past influences the characters and their interactions with each other. They can both get dark and violent, but Kamisama Dolls, despite having comedic moments, is the darker of the two, and contains more action. 

Both animes are about a love triangle, with two girls and a guy. The main guys have a similar personality, very cold and serious, but change through the series when they realise the meaning of love and friendship.In both, the main girls start as rivals but then become good friends. There´s also a lot of similarities between the main girls Shiika and Kuu, who are fragile girls that are being chased because they are the most powerful beings and dont want to release their powers. Both have action and a lot of drama and tragedy.  

Mushi-Uta kinda reminds me of Venus Versus Virus. The Virusses in VVV are replaced by Mushi's (bugs) in Mushi-Uta. Shiika kinda reminds me of Sumire, both the innocent and the types that don't wanna hurt other people, Rina reminds me of Lucia, a very strong girl who doesn't really show her feelings and also a leadertype. And than, the gun from Daisuke(Kakkou) and the guns from Lucia and Sumire. I think that you would like both animes, at least, I do! 

Yet another show where you've got certain people suddenly developing powers, factions of them grouping together, factions of humans trying to control or eliminate them, and various protagonists on the different sides. Similar at least in terms of the super-powers and the not-quite-making-sense-ness of it. 

Certain people have strange abilities that manifest as somewhat robotic-looking creatures that fight for them. In particular, both shows seem to have factions fighting against one another. 

Both have the same idea. In Mushi-Uta, the Mushi (insects) are able to consume people's dreams and thoughts. In Tegami Batchi, the Gaishou (also insects) eat people's feelings and emotions. After they devour people's thoughts and feelings, people become like dolls! They don't talk, speak, or show any reactions. They are alive but dead inside!