In Hamlet, are Hamlet and Claudius equally dangerous in rivalry?
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.
Absolutely they are equal rivals. A critical component of the Tragic Hero, he must face an antagonist who is his equal in power and cunning. Claudius also establishes the requisite counter-plot in Hamlet: he plots against Hamlet at each turn, by spying on Hamlet and Ophelia, hiring Rosencrantz and Guildenstern to spy on Hamlet, allowing Polonius to spy on Hamlet and Gerturde, sending Hamlet to England (to his death), and conspiring with Laertes to kill Hamlet in the final scene.
Without Claudius's interference in Hamlet's slow - but progressing - revenge plan, the plot would have had far fewer conflicts and complications and would have been less dynamic.