Other than being generally gullible, Malvolio's and Sir Andrew's characters are generally very different. To be gullible is to be easily tricked into trusting or believing someone. However, more importantly, it's really two different character traits they possess that make them gullible, or feed into their gullibility.
For Malvolio, his arrogance feeds his gullibility. Arrogance is an excessive feeling of "self-importance" or "pride" in one's self (Random House Dictionary). Malvolio sees himself being admired by others, especially Olivia, which makes him believe he is superior to others around him, especially the other servants. We especially see Olivia displaying admiration or appreciation for Malvolio in the very first act when she asks his advice as to whether or not she should continue appreciating Feste as a fool. Malvolio feels himself to be so superior and at such an equal level with Olivia that he actually dares to insult Feste's abilities as a fool. It is this same sense of superiority that leads to Malvolio's downfall, making him able to believe so easily that Olivia is in love with him and wants to raise him to her social status through marriage. We first see his gullibility as a result of his arrogance when we learn in Act 2, Scene 5 that Maria planted verbal seeds to make Malvolio begin to believe Olivia is in love with before actually planting the letter. It is his arrogance that makes him so quickly believe Maria, as we see in his lines:
'Tis but fortune; all is fortune. Maria once told me she [Olivia] did affect me: and I have heard herself come thus near, that, should she fancy, it should be one of my complexion. (II.v.21-24)
In contrast, Sir Andrew is actually not arrogant. In fact, he is really one of the only humble characters in the play. Literary critics have pointed out that he shows his humility in the very first act when he declares he wishes he was more intelligent and educated than he is now. We especially see him expressing this wish in the line, "Oh, had I but followed the arts!," rather than becoming a knight, which is basically to say he wishes he had pursued more studies, like the study of foreign languages (I.iii.87-88). He further shows his humility when, in contrast to Malvolio, he expresses his wish to be admired by reflecting that in the past, he was once admired, as we see in his line, "I was adored once too" (II.iii.166). Hence, in contrast to Malvolio, it is not Sir Andrew's arrogance and ready belief in being admired that makes him gullible. Instead, as he states in Ac 1, Scene 2, it is really simply the fact that he is not very smart. He is not as educated nor as clever as Sir Toby, plus he has a natural sense of trust in his friends, which combined make him very gullible and susceptible to pranks.