What are the similarities between women of the 19th century and women of the 21st century?
This is an interesting question!
The situation of women has improved greatly as compared to the 19th century. Women have voting rights (in almost all countries, and Saudi Arabia will allow women to vote and run for office in 2015), can work, and have the right to property and education.
However, there are still some areas where conditions have improved but bias remains. A very good example is the wage difference between men and women. Understandably, women in the 19th century hardly worked outside the home, meaning that actual wage differences between men and women were high. In the 21st century, though women can have professional careers, they are still paid less than their male counterparts for the same job. Some recent improvements have taken place; an example is equal prize money in Tennis Grand Slams for male and female winners.
Another similarity is that women still look after the house and are mainly responsible for the upbringing of the children, though the number of hours they spend at home (on an average) has declined due to professional careers.
And unfortunately, in some cases, regression to the 19th century has taken place and worsened the lives of women. A very recent example is the status of women in Taliban-controlled territories and ISIS, where women have almost no rights and their plight is same as that of women in the 19th century.