Aguu: Tensai Ningyou

Both have puppets and puppet masters whom were at war with each other, where one side fights to survive, while in the other anime the ones were fighting were out to save souls of people.  

The same character predicament where normal everyday character, finds herself in something that she never expected. 

Both have the same characters whose life changes the moment they've got themselves involve with something that they never expected.  

The same supernatural anime where ordinary character one day finds him/herself getting involved with some supernatural mess that changes his/her life.