They both were given a object that brought out their curiosity. In Pandora's box, she was given the box but was not allowed to open it so that made her more curious. And in The Monkey's Paw, they were given the Monkey's Paw, and the dad was curious to see what it could do.
They were both warned about the object they were given. In The Monkey's Paw, they were warned that the Monkey's paw could do bad things. In Pandora's Box, she was warned not to open the box by Epimetheus because of the bad things inside it.
In one story there was one thing that happened, and in the other there were three. In Pandora's Box, the only major thing that happened was she opened the box and the evil things came out. In The Monkey's paw, there were the three things that happened with the wishes.
The evil in one story goes out somewhere else, and the evil in the other just stays within them. In Pandora's Box, the evil was released into the world. Where as in The Monkey's Paw, it was just spread around their household.