The difference between a single and double edge weapon depends on the weapon it's self. Most single edge weapon have more weight to them as well as size and the single edge is all that is necessary. While the double edge weapons or more for speed and attacking they are made for it movement capabilities and speed. I would rely more on the single edge for force and the double edge for movement.
Some swords do not have an edge at all. Claymores, two-handed swords and hand-and -a-half swords usually are unedged as they are more of a bludgeoning weapon. Edged weapons were broken more easily against armor. You would therefore batter your enemy until they could not stand and then ram the point of the weapon through the chest or throat. Other weapons such as the foil or epee were used for quick stabbing attacks and not used to slash at all. These were usually used on unarmored opponents. Even some daggers were unedged to be used to drive the point home through less armored or under armored enemies. They were usually used in the off hand to block and counter attack while the main hand used your sword.