Macbeth and Malcolm don't have that much in common, ultimately. They do both begin as nobles in the good graces of the King of Scotland, Duncan. Macbeth is, at first, a loyal thane who gets promoted by Duncan after a successful battle in Act I (Macbeth is awarded an additional title -- Thane of Cawdor -- for his efforts and leadership). Malcolm is Duncan's oldest son and is named heir to the throne in Act I. This occurs after Macbeth has heard the prophecies saying he will be king someday and has already begun thinking about killing Duncan to get there; hearing that Malcolm will be the heir throws a kink in Macbeth's incipient plans and he begins to see Malcolm as an obstacle.
For most of the play, Macbeth and Malcolm are antagonists. Macbeth kills Duncan in Act II, and Malcolm and his brother Donalbain flee (Malcolm to England and Donalbain to Ireland) because they fear their lives will also be in danger as Duncan's heirs. For a short time, this raises suspicion in Scotland that Malcolm and Donalbain may be the murderers (their flight makes them seem suspicious). Once Malcolm and his brother have left, Macbeth is crowned king and begins what will be an increasingly corrupt and violent reign. Macbeth becomes paranoid and ruthless, even killing his own best friend (Banquo) and the innocent wife and children of his political enemy Macduff, who is in England helping Malcolm prepare to battle Macbeth. Ultimately, Macduff kills Macbeth and Malcolm is crowned King. As the play closes, the other characters are optimistic that Scotland will now return to greatness and its people will again feel safe, as Malcolm will be a much better king than Macbeth was.
Personality-wise, the two characters are very different. Macbeth is ambitious and will stop at nothing to get what he wants. While he is loyal to Duncan at the start of the play, his character quickly devolves, and he does not appear to have any moral compass. On the other hand, in Act IV, a long conversation between Malcolm and Macduff reveals that Malcolm is pure-hearted and good. Though he could stay in England and live a comfortable life, he feels it is his duty to return to his homeland and restore it to his glory. Malcolm must undergo a dangerous war against the ruthless Macbeth to achieve this. He thinks more about Scotland than about himself. Macbeth, on the other hand, seems to only want to be king for the power and has not higher moral purpose.