Banquo may not have taken the witches' predictions as seriously as Macbeth initially, but he certainly does before his death. He learns that the prophecies have been fulfilled when Macbeth is crowned king, and he says to himself that if they came true for Macbeth, he might have reason to think that they could come true for him as well.
The difference in character between them is that Macbeth is willing to sacrifice his soul to help the predictions along but Banquo refuses to do anything that would make him lose his honour, break his allegiance to the king, or blacken his conscience (Act 2 Scene 1). He is very careful not to join forces with Macbeth because he already suspects him of having a weaker character, a suspicion that he reiterates in the beginning of Act 3 when he says he fears Macbeth "play'dst most foully" for the Crown. The fact that Banquo is concerned about how Macbeth got the crown reinforces what he has said earlier--he is willing to gain from the prophecies, but, unlike Macbeth, he is not willing to sully his soul or his reputation to get there.
One thing that you have to consider when looking at the differences in characters after they hear the predictions of the weird sisters is that Macbeth almost immediately has confirmation of their predictions when he is made Thane of Cawdor, while the prediction for Banquo is far in the future.
The immediacy of the fulfillment of the prediction for Macbeth makes it a reality for him, we see the shift from disbelieving at first to accepting their prediction of his fate. While Banquo never fully believes in their predictions.
Macbeth also chooses to tell his wife Lady Macbeth of the weird sister's predictions, when he talks himself out of killing Duncan she goads him into going forward with it by calling him a coward and less than a man. Banquo, to our knowledge, never discloses the weird sister's prediction to anyone.
Macbeth is quite fasincated by the witches' predictions. He wants to know more about their predictions. He has a love hate relationship with the predictions. He knows what he is doing is wrong but he still wants to commit those evil deeds so he can gain power.
Banquo, on the other hand, is not sure to take the predictions seriously. He sees that the predictions are not telling him the whole story. Banquo does not act on the witches' words; perhaps this shows his aloofness over them.