Hamlet and Claudius are indeed worthy adversaries, each very dangerous to the other. Although they function within different moral codes and act to achieve different agendas, they are both men of intelligence and determination. Hamlet and Claudius are both dangerous, in part, because they are skilled in strategy and deceit. Hamlet plans to unmask Claudius by staging a rewritten play, just as Claudius cleverly plans to deliver Hamlet to his death at the hands of the English. When that fails, he plans Hamlet's death in a duel with Laertes.
Claudius and Hamlet both maintain false appearances while striving secretly to destroy each other. Hamlet wears the mask of madness, while Claudius pretends to be his loving, concerned parent. Claudius is excellent in deceiving others; he had, of course, killed Old Hamlet and stolen the throne without having that deed come to light for some time. Finally, while pursuing their own ends, both men are effective in engaging others to help them while keeping their secrets.