Hamlet and Macbeth are both obsessed with death. They are both nobles. Both are doomed to be tragic heroes. They are different in many ways, though. Hamlet is younger, and he’s not married. He grapples with fears about questions about death, and Macbeth is obsessed with his own death.
The irony here is that because the names of the characters are identical to the names of the plays that contain those very characters, it's impossible for us to figure out whether you are talking about Hamlet/Macbeth the characters or Hamlet/Macbeth the plays. Because you did not italicize the names, however, it leads me to believe you are referring to the characters.
I know this is probably going to sound obvious, but it's really important to bring up that both of these characters are two of Shakespeare's most famous tragic heroes. The fact they are tragic heroes is a VERY important similarity!
As such (and to put the qualities of a tragic hero into one sentence), they are honorable men led to their deaths by a tragic flaw that they realize far too late. Yes, these two characters have completely different tragic flaws: Macbeth's is "vaulting ambition" while Hamlet's (whose tragic flaw is much more debatable) is often explained as inaction/intelligence (i.e. thinking too much).
In Macbeth and Hamlet, there are two women who agree to the destruction of another in order to make their lives more powerful. Both women, Lady Macbeth and Gertrude, are involved in plots to kill innocent kings. While it never directly states that Gertrude wanted Claudius to kill her husband Hamlet, she obviously wanted to marry him; otherwise she would not have married him. She so desired position and staus so she married him in a hurry.
Lady Macbeth is deliberate in her desire to see her husband crowned king of Scotland. She desires the power and prestige of being Queen of Scotland.
Both women are living with a horrible secret. If Gertrude does not know that Claudius killed her son's father, she does marry him knowing Claudius is her son's uncle.
The similarities between these two women are their desires for status and prestige. Both women are living with murderers. Both women desire to be powerful.
Both women die during each husband's term of being king.
There is a deeper connection between these two women. There husbands are guilty of murdering kings in order to take over the position of kingship.
The question is whether or not both women were in on the plot to murder the kings.
There is a similarity, between Hamlets woman, Ophelia, and Macbeth's woman,Lady Macbeth. They both love them, and at the end they "became" crazy, and both commit suicide! But, the contrast between them:
1. Ophelia is the one beeing manipulated, and Lady Macbeth is tho one hwo manipulates.
2. Lady Macbeth desires to have more power, while Ophelia, doesn't really want that kind of power.
I think that's it!!