They each either take or are given a gift that they will be curious to find out what it is. In "Pandora's Box" Pandora is given a box from the gods and she is very curious to see what is inside of it. In "The Monkey's Paw" Mr. White takes a monkey's paw from the sergeant and he is very curious to see if it works.
Another similarity is that both of their curiosity led to misfortune. In "Pandora's Box" Pandora opens up the box and all of the evils of the world come out. Also in "The Monkey's Paw" Mr. White tries to use a wish to get more money his son ends up dying.
One difference is that Pandora was given the box and Mr. White took the box. This shows that Pandora might be a little more curious because it was a gift for her. In "Pandora's Box" It says that the gods gave Pandora the box as a gift which might make her more curious because the gift was meant for her. But in "The Monkey's Paw" the sergeant tells Mr. White to throw it into the fire but he does not listen and takes the monkey's paw.
In both stories curiosity controlled them. In "Pandora's Box" Pandora decided to hide her box so that she wouldn't have to think about it. In "The Monkey's Paw" Mr. White left the monkey's paw out which might have made him more tempted to use it.