Comparing these two well-known proverbs provides an interesting exercise in thinking. Traditionally, "the pen is mightier than the sword" has been used to express the idea that appealing to a person's logic and reasoning abilities would have a greater, more permanent impact on a popular opinion and individual thinking than simply bullying the public into action. Witness Thomas Paine's pamphlet "Common Sense", for example. With simple arguments and non-emotional language, Paine's booklet was quietly effective in shaping public opinion in the American colonies, and convincing people that the need to break from England prior to the American Revolution was less a matter of emotion and cataloguing Britain's wrongs against the colonies than it was a matter of "common sense", particularly when one recognized that the governing nation was an ocean away.
"Actions speak louder than words" is normally used to refer to a person's character or lack thereof; the idea is that a person can say anything he or she wants to say, but that a person's character and integrity is actually determined by how a person makes choices, treats others, and generally conducts his or her life. Applied to a international situation, however, "actions speak louder than words" might suggest that in fact the sword is mightier than the pen after all. Few people would argue that Osama bin Laden would have undergone a life-changing paradigm shift had the right people simply written him a rational brief explaining why his war on America didn't really make sense and asking him to turn himself in to accept the logical and lawful consequences of his crimes on 9/11.