The key difference between the way these two characters respond to the prophecies of the witches lie in the fact that it is Macbeth that chooses to act on their prophecies, giving in to his overriding ambition, whilst Banquo, although he clearly has ambitious thoughts, does not give into ambition in the same way.
Interestingly, the first time the witches appear to Macbeth and Banquo, Macbeth is startled by their predictions, but it is Banquo that says to Macbeth: "Why do you start, and seem to fear / Things that do sound so fair?" This shows that Banquo is definitely not averse at first to the witches' prophecies. However, this quickly gives way to doubt and scepticism, and later Banquo has troubled dreams regarding the witches and their prophecy, and says to Macbeth: "oftentimes, to win us to our harm, / The instruments of darkness tell us truths, / Win us with honest trifles to betray [us]." This is in sharp contrast with the increasing fascination and obsession that Macbeth (and his wife) have with the predictions of the weird sisters.
Interestingly, it is the ghost of Banquo that haunts Macbeth (rather than the ghost of Duncan), and one of the ghost's rebukes of Macbeth is how Macbeth responded to the witches' prophecies in comparison with Banquo. Thus the character of Banquo shows us that it is one thing to have ambitious thoughts (and don't we all), but it is something completely different to become a slave to ambition and be led into paths which involve committing murder and treason to satisfy the thirst of ambition.
Although the Witches wanted to meet Macbeth 'upon the heath', Banquo, accompanying Macbeth, chanced to see them first. Banquo was puzzled at their 'wither'd' looks and 'wild' attire; he doubted if they were 'the inhabitants o' the earth'; he alluded to their wizened appearance and their female sexual identity being contradicted by their 'beards'. As Macbeth asked them to speak, the three Witches made their proclamations.Banquo noticed Macbeth's immediate reaction--'..why do you start, and seem to fear/Things that do sound so fair?' He could also see Macbeth 'rapt withal'. Since the Witches welcomed Macbeth with 'present grace and great prediction/Of noble having and of royal hope', Banquo demanded his share of 'supernatural soliciting'. The Witches then greeted Banquo with prophecies, but in a language of paradox--'Lesser than Macbeth, and greater', 'Not so happy, yet much happier' & 'Thou shalt get kings, though be none'. Macbeth then charged the Witches for more, but they vanished into the air.
What followed in this scene--act1 sc.3--revealed the difference between Macbeth and Banquo in their attitudes to the Witches and their prophecies. While Macbeth took the Witches' predictions very seriously, especially that of kingship of Scotland, Banquo showed his scepticism and indifference. While Macbeth was so keen to have more, Banquo was incredulous of what he had just heard. Banquo advised Macbeth to be on guard against such uncalled-for well-wishing:'And oftentimes, to win us to our harm,/The instruments of darkness tell us truths,/Win us with honest trfles...'. The immediate fulfilment of one of the predictions effects a change in both, but still Banquo differs from Macbeth, and expresses his suspicion--'What! can the devil speak true?' However, it is not correct to say that Banquo was fully immune to temptation, for these lines suggest how Banquo fought within himself to smother his unscrupulous thoughts--'Merciful powers,/ Restrain in me the cursed thoughts that nature / Gives way in repose'.