Whether to murder Duncan is an issue Macbeth struggles with before committing the crime. Macbeth respects Duncan and decides he can't kill him. Then Lady Macbeth questions his manhood and convinces him that he must kill Duncan. Macbeth might have backed down if Lady Macbeth's ambitions hadn't been greater than his own at that time. Lady Macbeth was afraid that Macbeth's nature was too full "of the milk of human kindness". After the murder of Duncan, Macbeth is shaken, forgetting to leave the daggers beside the guards.
Macbeth decides to kill Banquo and his son because they are a threat to Macbeth's future as king. At this point, Macbeth has become a cold-blooded killer who will do anything to keep what he wants. Macbeth doesn't even tell Lady Macbeth about Banquo's murder; he has it done by hired killers without consulting her. He doesn't even take into consideration that Banquo is his friend, and he is truly blind with ambition.
Compare and contrast the murders of Banquo and Duncan
Well, a fully developed comparison would involve a bit more context. What are you comparing about these actions?
In general, though, you could say the following things about the two crimes.
Macbeth murders Duncan himself (with his wife's urging/help).
Banquo is killed by people Macbeth has set to the task.
As a result, Banquo's murder is much riskier politically.
Duncan is murdered in Act II; Banquo is murdered in Act III.
After Duncan is murdered, Macbeth seems to hold it together pretty well; he blames the guards. After Banquo is murdered, Macbeth about loses it in public.
After both murders, Macbeth's mind is disturbed. After both murders, the natural order of things is disturbed.
That should be enough to get you started on this question, yes?
Macbeth has many doubts that he could kill King Duncan and doesn't think he will be able to live with the guilt of assassination while the king is staying at the same palace. It makes him emotional-scarred in his heart and was confused and bewildered about what to do. I think Macbeth has a high sense of honor and moral integrity and to murder the king would be too great him for him without outside party help in assisting. It shows that he is not all pure evil and he stills has some conscience in his heart compared to Lady Macbeth
The situation changes 360 degrees in the murder of Banquo where Macbeth behavior took an complete change. There was no outside help from Lady Macbeth and all the decisions are Macbeth only. When he was king, his mind is still filled with power-hungry ambitions to control the whole empire and he felt that Banquo was the obstacle towards his success, so murdering him was a necessity. He became a cold-blooded and inhumane monster who would do any despicable things just to get his way. He was very low to appoint hidden assassins to sneak to his room to kill him, showing that he was a lowly-count coward who would do anything just to realize his mighty ambitions. This behavior of this completely contrasts his behavior and emotions during the murder of Duncan. The power of money and success surely got to his brain and make him power-crazy.