What similarities/differences are there between what Polonius asked Reynaldo to do and what Claudius asks Rosen. and Guilden. to do?

Concerning spying in Shakespeare's Hamlet, I'll focus on a different angle than the answer above.  Both Polonius and Claudius are characterized by their actions. 

Polonius is revealed as hypocritical and petty and as an interfering parent.  He has barely finished preaching to Laertes and telling him to be true to himself, when he arranges to send someone to spy on him.  Based on everything we see of him in the play, Laertes is a model son.  He is even respectful to an elder that is extremely hard to be respectful to--his father, Polonius.  Gertrude isn't.  She loses patience with his hyperbole.  The act of spying on his son is hypocritical and petty, and Polonius has no business doing it.

Claudius is revealed to be insidious and underhanded.  When he orders the interchangeable Ros. and Guil. to spy on Hamlet he may remind one of Macbeth in the tragedy named after him, when Macbeth says that he has spies in the houses of all of his thanes.  He may be wondering if Hamlet is "mad," but this is secondary to his wanting to keep an eye on Hamlet in order to protect himself. 

Claudius, though highly intelligent and capable, also makes a mistake here by underestimating Hamlet.  Hamlet sees through his plan, humiliates the two spies, and reveals to Claudius only what he wants to reveal to Claudius.