Duncan and Malcolm, in Shakespeare's Macbeth, are of course father and son, and similarities do exist between the two. I'll detail one of those similarities for you.
Both are wise leaders, with the son, at least in part, learning from his father.
After Cawdor is executed, Malcolm tells the king (in Act 1.4) that Cawdor died nobly, that "Nothing in his life/Became him like the leaving it." Malcolm is impressed that a man guilty of such treachery could die so nobly. Duncan replies:
There's no art
To find the mind's construction in the face.
He was a gentleman on whom I built
An absolute trust.
Duncan is wise enough to know or at least to have just learned that you can't judge what a man is thinking by his facial expressions. Malcolm learns this lesson and uses it when the time comes for him to seize his place as king. In Act 4.3, Macduff arrives in England hoping to join Malcolm in a civil war against Macbeth, but Malcolm knows better than to trust him just because Macduff says he is Macbeth's enemy. When Macduff arrives and tells Malcolm how terrible things are in Scotland under Macbeth's rule, Malcolm tells Macduff:
What you have spoke, it may be so, perchance.
This tyrant, whose sole name blisters our tongues,
Was once thought honest. You have loved him well;
He hath not touched you yet. I am young, but something
You may deserve of him through me, and wisdom
To offer up a weak, poor, innocent lamb
T'appease an angry god.
Malcolm cannot be sure of Macduff because Macbeth was once thought to be honest, Macduff has loved him in the past, and if Macduff were to betray Malcolm he would certainly be rewarded by Macbeth. Plus, Malcolm says, Macduff has not yet been harmed by Macbeth, which suggests he may be Macbeth's ally.
Malcolm then proceeds to put Macduff through an extensive and creative test to see if he really is loyal to Scotland. Malcolm pretends to be excessively lustful, excessively greedy, and an all around worthless human being. When Macduff announces that a man such as Malcolm has described is not only not fit to rule Scotland, he is not even fit to live, Malcolm knows he's got the right man.
Unfortunately for Duncan, though he was wise, he was also gullible, and he makes the same mistake with Macbeth that he made with Cawdor. Malcolm does not make the same error. And when news comes from Scotland that Macduff's family has been murdered, Malcolm's trust in Macduff is verified.