Both Macbeth and Banquo, military leaders in Scotland, have thus far, by all indications, lived their lives in honor and service to their king. This service was the focus of their ambition until the encounter with the Three Weird Sisters.
In the prophecy, Macbeth is predicted to become king, while Banquo is told that it is his children who will ascend the throne. The nature of these prophecies perhaps regulate the reactions of the two different men.
Banquo is not told anything about himself, but only his children. Therefore, he does not have an immediate vested interested in taking action to fulfill the prophecy. Macbeth, however, does have an interest and takes upon himself the responsibility to bring it to fulfillment, rather than let Fate take its course.
Banquo, in discussing the prophecy, expresses doubts as to the validity of such a thing, coming as it does from witches. While he admits that it might contain some element of truth, he is wary that its way is to lead them to evil, rather than success. In this, Banquo shows a level of wisdom and insight that Macbeth does not possess.
Banquo's refusal to take action in fulfilling the prophecy conflicts with Macbeth's choice to do so, aided by his wife. This puts Banquo in a dangerous position, especially since, according to the prophecy, it will be Banquo's children, not the children of Macbeth, who will succeed Macbeth. Unsure of this aspect, Macbeth is taking no chances and murders Banquo as well as Duncan.
I liked this question! We need to look at the start of the play when they are both 'captains' and 'worthy' men. They are essentially loyal lords to King Duncan and have helped to defeat the invading forces. Both men are presented therefore as courageous and determined and have the thanks of the old king and the respect of other men. After the witches speak to Macbeth, Banquo bids them speak to him, because he is naturally curious about them and what they may have to say to him. But Banquo does not head into some dreamy state of reflection as Macbeth does, he doesn't lose himself in the prophesy. What the prophesy does is 'tie' Banquo to Macbeth after the murder of Duncan, he feels Macbeth has a golden motive for the deed and considers that Macbeth may have 'played most foul for it,' but he does nothing, perhaps because he is a part of the events that are unfolding, and he hopes his child will one day be king. Banquo only appears in the first part of the play as he is murdered before the coronation feast, so he never turns as Macbeth does to evil. He of course never has a Lady Macbeth character in the background to spur him to an evil path and he does sacrifice himself to save his son. Macbeth has no children so has no such attachment for another. Banquo is more of a family man and less motivated by self interest, more for the wider concerns for his sons advancement.
Hope this helps!