What are the differences between Portia and Jessica as revealed in the play "The Merchant of Venice"?

The differences are subtle and come mostly from the different situations the two women find themselves in.

Portia and Jessica have much in common.  Both are beautiful, intelligent, and funny.  Both are bold and can be blunt (e.g. Jessica says, "Our house is hell," Act 2 Scene 3; Portia says, "There is not one among [my suitors] but I dote on his very absence," Act 1 Scene 2).  Both disguise themselves: Jessica as a page...

The differences are subtle and come mostly from the different situations the two women find themselves in.

Portia and Jessica have much in common.  Both are beautiful, intelligent, and funny.  Both are bold and can be blunt (e.g. Jessica says, "Our house is hell," Act 2 Scene 3; Portia says, "There is not one among [my suitors] but I dote on his very absence," Act 1 Scene 2).  Both disguise themselves: Jessica as a page boy so that she can run away with Lorenzo, Portia as a lawyer so that she can save Antonio's life.  

The biggest difference between the two is that Portia saves the day by playing the part of "Balthasar," a "Doctor of Laws," so that through her brilliant and humane arguing in court, she saves Antonio from having to give a pound of flesh to Shylock, Jessica's father.  From this we can see that Portia is very well-educated, wise, and generous of spirit.  She is also very self-confident, willing to pull off this dangerous undertaking without even telling Bassanio what she is up to. 

Now, Jessica is not stupid, but we get no hint from the play that she is as well-versed in the law as Portia.  She is wise and kind, but her bold move (running away with Lorenzo) is done mostly for her own sake, not to save someone else.  She is brave, but not as bold as Portia.  She runs away with Lorenzo at night, and even then she does not want to hold a torch for fear she be seen in her pageboy's costume (Act 2, Scene 6).  

Jessica is a plucky woman trying to escape a bad home life.  We can infer that her life with Shylock did not offer as high a standard of living, nor quite as good an education, as Portia received.  She also has a graceless tyrant for a father, whereas Portia's father (now deceased) was apparently very wise.

Jessica is using her virtues to rise above the situation she was born into.  Portia, an aristocrat, was born with many privileges that allowed her to develop her natural gifts.  Now she is using her advantages to help others.