Julia is presented by Webster as very much the foil to the Duchess. Whereas the Duchess is given to us as a respectable aristocratic lady of the utmost refinement and constancy, Julia is portrayed as a scarlet woman, brazen in expressing her overpowering sexuality. She's an inveterate pleasure-seeker, flitting back and forth between one man and another whenever the mood suits her.
It's clear from Julia's unpleasant demise—murdered by her lover, the Cardinal, using a poisoned Bible, no less (how's that for symbolism?)—that Webster does not regard her behavior as in any way appropriate. The prevailing moral standards of the time dictated that women, especially those of noble birth, should maintain chasteness and purity at all costs. Julia, in departing from those standards (and that's putting it mildly) has suffered what most people at that time would've considered a richly-deserved fate.
In stark contrast, the Duchess's fate is truly tragic because, unlike Julia, she unfailingly lives up to the ideal of aristocratic womanhood. Despite the constant taunts and accusations from her brothers concerning her clandestine marriage to Antonio, she can hold her head up high as a virtuous lady of quality. Though possessed of a powerful sexuality, the Duchess chooses to express it within the confines of marriage, albeit a marriage with a man some way beneath her on the social ladder.