In Shakespeare's Macbeth, Macbeth and Banquo have to struggle against several things.
At the play's beginning, Macbeth and Banquo have both struggled in the war between Scotland and Norway, fighting a fierce battle to defend Duncan and his kingdom.
Later in Act One, while returning from the battle, Macbeth and Banquo meet three witches that give both of the men predictions. Each struggles with what the women say, but at different times. Macbeth wants to believe what the Weird Sisters have to say because he likes what they have to tell him:
All hail, Macbeth, that shalt be King hereafter! (I.iii.53)
Until this point in the story, Macbeth has been a loyal subject, a fierce warrior for Scotland and well-pleased with his lot in life. At first Macbeth struggles with the idea of killing Duncan and decides to end his plans, but his wife bullies him into continuing. Eventually Macbeth will admit to possessing a dangerous ambition, and it is this character flaw (and his wife's nagging) that drives him to eventually kill Duncan: his king, cousin, friend and houseguest. He does this because he wants to be King of Scotland.
Banquo, on the other hand, is not concerned with what the witches have to say to him because he chooses not to pay attention to them. He knows that these women are evil and would love nothing better than to trick both Banquo and Macbeth into doing something that would cost the men their eternal souls. (Shakespeare's Elizabethan audience would have believed these things completely.)
However, after Duncan is murdered in Macbeth's house and the King's sons flee for their own lives, Banquo struggles with the witches earlier predictions, and he begins to have suspicions about what has transpired because he recalls what the witches had predicted for Macbeth. Banquo grows ever more convinced that Macbeth had a hand in Duncan's death:
Thou hast it now: King, Cawdor, Glamis, all,
As the weird women promised, and I fear
Thou play'dst most foully for't… (III.i.1-3)
Macbeth knows Banquo well: they have been great friends in the past. Macbeth knows that Banquo is a man of integrity who will be unable to remain silent if he believes Macbeth was complicit in Duncan's death. Knowing this, Macbeth realizes that he has sold his soul for the throne (for it was believed to be a mortal sin to kill a king), but will be unable to enjoy it because he fears exposure at the hands of Banquo. Macbeth's fear of Banquo ruins his enjoyment of his new position and preys on his mind. He struggles with the knowledge that Banquo holds information that could wrest the throne from his possession:
To be thus is nothing,
But to be safely thus. Our fears in Banquo
Stick deep, and in his royalty of nature
Reigns that which would be fear'd. (51-55)
Banquo's noble character—his sense of honor that he will not betray for anything—is dangerous to Macbeth's continued reign. So Macbeth makes arrangements to have Banquo (and his son Fleance) killed while out riding, prior to Macbeth's banquet.
Macbeth and Banquo struggle in battle while fighting side-by-side, but the struggles they face because of their very different characters drive Macbeth to murder his friend, as he murdered Duncan.