This is a challenging question, primarily because I don't really think it is true. If you create a two column chart for Polonius and Claudius you can start to brainstorm -- from there you may be able to make something of a thesis for your essay.
Here are some things they have in common:
Father (figures) -- Claudius to Hamlet -- insincere love for him; eventually feels threatened and wants him killed. Claudius wants Hamlet to stop the public display of mourning because it reflects badly on Claudius and he is concerned with his reputation. On the other hand you have Polonius to Laertes and Ophelia. In regards to Laertes, he probably loves his son, but his only interaction is a long list of advice about Laertes behavior with a common theme of watching his reputation. The same could be said for his relationship with Ophelia. He may love her, but he is using her to learn about Hamlet so that he can look smart to the king, and he is concerned about how her behavior will reflect on the family's reputation.
Other things they have in common: sneaky, sly, arrogant
After that, I don't think there is much to say about how these two men have anything in common. What you could analyze is Hamlet and Laertes and their need to avenge their fathers' murders. This is where the plots mirror one another. Both men are justified in their actions and are determined to follow through with their revenge. Both Polonius and Claudius end up dead because of the behavior of the sons and the plot events that lead to these accidental and miscalcuated deaths.