These are two very interesting characters to examine when thinking about the theme of independence. You might want to consider the following issues when comparing and contrasting them:
1) Both Nora and Juliet show their independent spirit by the way that they rebel against the various expectations of society of the day. Firstly, Nora leaves her husband and children which would have been unthinkable in her time. Secondly, Juliet defies the wishes of her parents by marrying the man she loves rather than the man they have prepared for her to marry.
2) A big difference is of course the way that Nora is only able to find her independence outside of marriage, whereas Juliet exerts her independence through choosing who she will marry. She still is not truly independent, because she would have been subject to her husband.
3) Lastly, and this is really a development of the second point above, you need to think how these two characters' acts of independence are presented. Nora's slamming of the door as she leaves her marriage and life behind at the end of the play is really an attack on social roles and conventions of marriage at that time. For Juliet, her act of independence is an attack on parental control and a victory for love.