There was a time when advancements were made first by the sword, then by the mind. (Think of how many events in history involve "battle" or "conquest.") However, the most successful advancements were made in conjunction with strategy and planning and innovations--all products of the mind. I, too, vote for mind over sword.
I would also say that the mind contributes more to human progress than the sword. The above poster uses two great examples of that in King and Ghandi. Also if you think about all the advancements in technology over the years, that would also be an example of the minds contribution.
I sincerely believe that the human mind contributes far more to progress than the sword. At the risk of overusing a well-worn example, Gandhi and Martin Luther King, Jr., demonstrated for all time that nonviolent civil disobedience can launch revolutions.
Nevertheless, there are also examples of the sword accomplishing what reasoned discourse never could. Would Hitler have been willing to sit down and listen to an explanation of why his schemes were unconscionable? Of course not. It was only due to the a massive war effort by the Allies that the Axis powers could be brought to heel.
In my opinion, human progress is more dependent on the mind. The growth of particular nations may well be dependent on the sword, but the progress of humanity as a whole is much more dependent on the mind.
I cannot think of anything that really benefits people that has directly come from "the sword." Sure, the need for war has led to some inventions like the rocket and radar and nuclear energy. However, those things still really came from the mind. They were conceived of by people who were using their brains.
Beyond that, though, there are all sorts of things that have been devised that help us progress that were not really created for war. I think those things (ideas like democracy, things like art, tangible stuff like air conditioning) have contributed more to our growth than war has.