I would like to know your opinion of which law school is better between these two, Duke or Georgetown?

Both schools are very good schools, you should feel lucky on considering both of them, good job.

From my point of view, Duke will provide you with a deeper knowledge in law, it will be more academic. On the other hand, Georgetown has more of an international name, which will also help in your career.

It also depends on what type of law you want to focus. For example, Georgetown is very good in International Law (ranked 3rd in USA) and in Tax.

Look at this link http://www.llm-guide.com/law-school-rankings, here you will see some rankings depending on the type of law you would like to study, Georgetown is pretty high. Also washington is a very nice city.

Just remember, there is no wrong choice between those two.

Best of Luck.