The Chi no Ryu are the organisation fighting for the destruction of mankind. They believe that humanity have done enough damage to the Earth and that the planet would be better off without them, so it can recover.
Like the Ten no Ryu, the Chi no Ryu live lives outside their organisation. Although the anime portrayed them as being wholly devoted cold-blooded killers (the anime appears very biased in favour of the Ten no Ryu, whereas the manga appears far more impartial), in the manga they all have jobs and almost seem to view the whole Chi no Ryu organisation as more of a part time job than a devotion.
For example, Yuuto is not only skilled in the use of lightning, he is a public service official. Satsuki not only controls the monstrous supercomputer, The Beast, she is a student who prefers only the company of the computer she created. I feel that it's this depth that gives the manga an extra advantage over the anime.