Rozen Maiden: Träumend

Same way as in Rozen Maiden we have the chosen warriors (females) who have to fight each other in order to achieve the final goal. Some characters argue with each other but over all everyone live peacefully until a new mysteriouse fighter appears and starts the disaster and by that all HiMEs are forced to forget about peaceful life same way as Rozen Maidens. The easy going life turns into nightmare full of sorrow and pain. 

The first 2 Rozen Maiden seasons together are very similar to Mai-HiME. Both shows are character-driven; we can see how the different personalities and attitudes of the characters fuel their interactions and decisions. Drama is present in both shows, although there is a good amount of comic relief as well. Both series include battles, although there is more action in Mai-HiME. While the two series are lighthearted at first, they become darker and sadder as the plots progress. 

Although both anime are different in character design and style, they relate to each other the fact that there is a prize to be won in a battle royal. Magic and fantasy themes also play a role in both series.