The first thing is that they both had consequences for their curiosity. In the story the Monkeys Paw the family is curious about making three wishes with the paw and it ends up making their life miserable. In Pandoras box when she opens the box because of her curiosity all the evil and bad things fly out into the world terrorizing people.
The second thing is that they both got objects that caused them to become curious. In the story The Monkeys Paw a solider brings them a paw that can grant them three wishes which makes them very curious. In the story Pandoras box the Gods give Pandora and Epimethius a box that can not be opened.
In both stories curiosity ruled. But in Pandoras box Pandora hid a box under her bed to try to stop her curiosity. In the other story they character just let the Monkeys paw around in the open.
In the stories people die that are close to the characters than in the other that are not. In pandoras box when she opens up the box all the evil stuff begins terrorizing people but they are not clode to her. In the Monkeys paw because of the curiosity a character dies because of that.