Unfortunately, their axes and swords didn't do much good when their opposition had artillery.
Also, one of the great heroes of the American Revolution, Gen. Hugh Mercer, was at Culloden, and because he was hunted after the battle, fled to America. He originally settled in Pennsylvania, met George Washington during the French and Indian war, became a friend of Washington's and died a hero during the battle of Princeton. Gen. Patton was a direct descendant of Hugh Mercer.
Mercer County in New Jersey is named after him.