What is revealed about Macbeth and Lady Macbeth's character from their conversation about killing Duncan?

Macbeth is more temperate in his actions and Lady Macbeth is ambitious and ruthless.

From Macbeth’s reaction to the witches’ prophecies and his anger at being passed over for the kingship, you would think that he would be ready to slay Duncan at the first opportunity.  However, by the time he returns home he has cooled off and come to his senses.  He is now worried that killing Duncan is not a good idea.

Lady Macbeth and Macbeth argue about killing Duncan.  Macbeth is worried about the consequences of such a risky act, and also about the fact that Duncan has done nothing wrong.  Duncan is related to him, and his guest.  How can he kill him?

He's here in double trust;
First, as I am his kinsman and his subject,
Strong both against the deed; then, as his host,
Who should against his murderer shut the door,
Not bear the knife myself. Besides, this Duncan
Hath borne his faculties so meek, hath been
So clear in his great office, that his virtues
Will plead like angels, trumpet-tongued, against
The deep damnation of his taking-off … (Act 1, Scene 7)

Lady Macbeth is not happy that her husband is getting cold feet.  She has a plan, and she wants to make sure that he sticks to it.  If her husband is going to be king, this is the only way. As long as she takes charge, everything will be fine.  As Macbeth begins to falter, she insults him to shore him up

MACBETH

If we should fail?

LADY MACBETH

We fail!
But screw your courage to the sticking-place,
And we'll not fail. (Act 1, Scene 7)

She tells him that if he has enough courage, they won’t fail.  While Macbeth is wavering, Lady Macbeth is brutal in her evaluation of him.  She earlier claimed that he was “too full o' the milk of human kindness” (Act 1, Scene 5) to do what needs to be done.  Lady Macbeth thinks that she is the man in the relationship.

When you durst do it, then you were a man;
And, to be more than what you were, you would
Be so much more the man.  (Act 1, Scene 7)

So while Macbeth may be ambitious, he is also not as courageous as Lady Macbeth.  She is the one that develops the plan and makes him stick to it.  She browbeats him into going along with it, and makes sure that he does everything as she has instructed.  Macbeth also has some moral scruples, feeling that killing Duncan is wrong.  Lady Macbeth wants what she wants, and she will do anything to get it.

The ironic thing is that both of them fall apart after killing Duncan. When Lady Macbeth sees the body, she feels remorse.  Macbeth feels guilt, but he also succumbs to paranoia.  Now that he has the crown, he is worried about keeping it.  In the end, both of them are destroyed by their lust for power the guilt resulting from their actions.