Magnussen knows that Moriarty is one of Sherlock's pressure points, so he collars him and keeps him on a leash to prove his power to Sherlock.

He also knows that even Jim Moriarty has a pressure point, though; and so he collars Sebastian Moran, too, because he quite enjoys having a matched pair at his heels, and it amuses him to watch how Moran continually (futilely) tries to protect Jim.