Mai-HiME, Selector Infected WIXOSS Recommendations
1. Both shows involve a power that only girls can use: In SIW, characters can summon "LRIGs" (card avatars) to play in card battles while in Mai-HiME they can summon "Childs" (mechanical monsters) to help them fight.
2. Using this power comes with risks.
3. Characters fight for something they hold dearly.
4. Both shows get progressively darker.
Although the settings and circumstances are different, if you like one anime, I think you'll like the other! :)