The women's rights movements in both Britain and the United States focused on obtaining political rights, particularly women's suffrage, in the first two decades of the twentieth century. Both were successful in using the democratic rhetoric and the social changes of World War I to further their cause, though suffragettes in America were more vocal during the war itself. The Nineteenth Amendment gave all women the right to vote in the United States in 1920, and some women in Britain were extended the franchise in 1928, with universal suffrage coming ten years later.
Generally speaking, the movement for women's rights was more radical in Britain than in the United States. Women like Emmeline Pankhurst led protests that were sometimes violent in nature, including arson and hunger strikes. They tended to favor direct action over political lobbying, at least until World War I. In the United States, violent tactics were seldom used, though some suffragists like Alice Paul adopted more radical tactics after visiting her counterparts in England.
My answer above says that "some women in Britain were extended the franchise in 1928." It should read "1918."
In 1928, all women in England over 21 were granted the right to vote. Only women who owned a certain amount of property were given the right to vote in 1918.