Eliza Doolittle is a dirty, lower-class, uneducated girl who sells flowers for a living.  No one gives her much of a glance, and even Higgins and Pickering wouldn't have taken a second look at her had it not been for the "dare" they set up between themselves that they could transform the helpless little guttersnipe into a gloriously articulate thing of beauty whom no one would guess came from the gutters of London.  Eliza is a nobody...she is perceived as weak, poor, no power.  She does hold her own, but not until much later in the play when she asks the question, "What is to become of me?" She eventually decides to marry Freddy, when the overall understanding is that she and Higgins have fallen in love.

Medea, on the other hand, is wealthy, educated, and very powerful indeed.  She has a strong-willed and determined to get her way.  So much so, that she murders her children in order to cause pain to her husband.  Although this is a crime, one must admit there is a certain strenght of resolve and determination to carry out such an act.