Dennou Coil, Shinsekai yori Recommendations
Both are about a group of children with special powers fighting the system and searching for their purpose.
Both have the same eerie atmosphere plus strange mixture of sci fi and some supernatural mystery.
Both series has that mysterious aura feeling to it involving a group of children in a futuristic world. In that world, there is supernatural events that is surrounded with mystery.
There exists a theme of science fiction involving the power of the mind in both series and dealing with a "system".
Both series' cast of characters have similar age groups with developed knowledge of their abilities.
-Children grow up and learn more about their world
-Everything is not as it seems, both anime get pretty dark at times
Both shows treat their female characters very well and are set in rich, well-constructed, dystopian worlds. They both have mysteries at their core which are really well-written.
Strange occurances in a futuristic and different science fiction-based world, and a group of kids are left to uncover the mysteries on their own. Things are not what they seem.
Each group in each show has powers, or enhancements.
Odd technological creatures that shouldn't exist in the world, but do.