There is one definite connection between Death Wish and Hamlet. The tool of vengence is not a perfect tool of justice.
As pointed out above, the character of Hamlet is destroyed and consumed in his role as the the Figure of Revenge. He is not "good" or innocent. This is true of Bronson as well. However righteous his rage may be, Bronson's character chooses to cross the line and defeat evil with evil.
We might argue that justice is done in both stories, but this justice is not carried out by a white knight but by a sullied individual who, so sullied, has nothing left to lose morally.