Do you think Hamlet is any better than Claudius given Hamlet's murder of Polonius and Claudius's murder of the king? Are their stories of ambition and passionate retribution different?
Hamlet might have racked up a greater body count than Claudius but Claudius definitely performed the greater crime. Claudius actions were pre-meditated murder, followed by adultery whereas Hamlet always acted in the moment, driven by his passions which were ignited by Claudius. In a sense Claudius is partially responsible for Hamlet murdering Polonius. He killed his father. He married his mother. He turned his best friends into spies and conspired with Polonius to have Ophelia turn against Hamlet. After all this, he has the audacity to act as surrogate father towards Hamlet. Had none of these events occurred, Hamlet would never have been driven to the lengths he went.
Also, I’d argue that Claudius was driven more by ambition than passion. Otherwise, his passion would have overturned his desire to be king when racked by guilt. Had he really been sincere about his guilt over killing his brother, he would have divorced his Gertrude, given up the kingdom, and submitted himself to justice. Throughout the play, Claudius is driven by his ambition, whereas Hamlet gives up so much to avenge his father. He sets aside his ambition to follow his passions.
So I’d say their motivations are significantly different, especially since Hamlet kills both Laertes and Claudius in self-defense. Yes, killing Polonius was grievous, but not pre-meditated, as opposed to Claudius murdering Hamlet Sr. Hamlet is driven by passion. Claudius is drive by ambition