One similarity is in "The Monkey's Paw" they treasure the paw and are curious about what is going to happen. Another similarity is they keep a dangerous object with them and around them all the time. Same thing with "Pandora's Box", Pandora left the box in her room were it was easily accesible and can be opened at any time.
In both "Pandora's Box" and "The Monkey's Paw" something bad happens because they acted on their curiosity. Pandora lets out all the evil that was in the box out into the world. The Dad in Monkey's Paw wishes for 200 pounds, but his son ends up dying, then he gets his wish. So this shows how something evil/ bad happened.
In "Pandora's Box" Epimethius made Pandora but the box under the bed. He also made sure she didn't think about, so nothing bad would happens. Another difference was it was given as a gift and not to be opened, but curiosity ended up controlling her actions.
In the "Monkey's Paw" they left it on the table and was open for anyone to take. Another difference is they retrieved the paw, after the Sargent threw the paw into the fire. The Finally difference is Everyone was allowed to hold it and keep it with them.
Another difference compared to "Pandora's Box" and The Monkey's Paw" is the son was holding the paw, while Pandora let the box hide under her bed. There are many differences in the story, but even though they got this as gifts and were told not to do anything with it, they still let curisosty come over them and control their actions. A difference though, is that, each time they made a wish it never turned out the way they wanted.