The most obvious similarity between the two stories is that they both deal with the savagery of a group of boys. In "The Destructors," an urban street gang willfully destroys an old building that has stood for hundreds of years. In Lord of the Flies, a group of schoolboys crash-land on a remote desert island, where they quickly degenerate into savagery and turn on each other.
Social class is an important theme in both stories. In "The Destructors," the Wormsley Common gang consists of poor, working-class boys who have nothing; they have no money, no real family to speak of, and certainly no education. Nevertheless, the gratuitous act of vandalism and destruction they carry out is inspired by their new leader Trevor, who, unlike them, comes from a good home and really ought to know better. Trevor abuses his position of leadership to incite the other boys to commit a serious, and utterly needless, criminal act.
A similar abuse of leadership is practiced in Lord of the Flies by Jack Merridew. Like all the boys on the island, he comes from a privileged, elite background. As a scion of a good family, he really should know the value of a well-structured, ordered society. But before long, he disregards all notions of order to make a shameless grab for dictatorial power. In doing so, Jack has derogated from his duty as one of society's natural leaders to transform himself into a blood-crazed savage.
Ralph and Piggy, on the other hand, though from the same social background as Jack, do take their responsibilities seriously. They know that civilization is something that has to be painstakingly built and preserved over time if it is to endure. Even when civilization is sustained, as in the England of "The Destructors," barbarism is never very far away. Thus, it is necessary that the privileged classes exercise responsibility along with their power.