Night Head 2041

Both take place in the future and in both anime the world is messed up and broken because of the psychic abilities of some humans. The darkness in both is very similar but night head 2041 looks and I think is more futuristic than Shinsekai Yori even though it takes place before that. 

Psychic powers, brotherly bonds, pasts shrouded in mysteries and truths hidden in human mind. 

Futuristic setting with science winning over faith. Rebellion and supernatural powers with action in both. 

3DCG sci-fi series in which the protagonist(s) find themselves a dozen or so years further in the future, in a world where the military has more control. The protagonists in both shows are part of a special military team tasked with finding people who would harm the peace, and even have the potential to destroy the world - that being psychics in Night Head 2041 and people with physics law-breaking weapons called Ex-Arms in Ex-Arm. The protagonists in both shows are also that which they are trying to destroy - psychics and an Ex-Arm. The plot in both shows can get equally convoluted.