In Othello, how does Othello's description of Desdemona's personality and behavior differ from Brabantio's image of her?
I assume you are refering to Act I scene 3, which is of course when Brabantio bursts in on the Duke claiming that Othello has tricked his daughter into loving him. What is interesting about the way that both of these characters describe Desdemona is that it is her father seems to lack understanding about Desdemona and her personality. Notice how he expresses his incredulity about Desdemona ever managing to fall in love with Othello:
A maiden never bold,
Of spirit so still and quiet that her motion
Blushed at herself; and she, in spite of nature,
Of years, of country, credit, everything,
To fall in love with what she feared to look on?
Brabantio makes out his daughter to be a timid creature who would never approach Othello and who would be terrified of him. By Othello's account, however, it was Desdemona that sought him out and implored him to share more of his history. Othello says that she would come again and again, "with a greedy ear" to "Devour up my discourse." Othello presents Desdemona as being the one who sought him out and pursued the relationship, whereas Brabantio presents Desdemona as being a silent, timid recluse who was corrupted and beguiled by Othello's "arts."