Where bigger, more powerful brakes make the difference is in two places: Long downgrades and heavy loads. Discs run cooler for longer than drums, generally speaking, and cool brakes work better. That being said, once you lock up your tires in a panic stop, you have relinquished control and your stopping distance increases. Under certain conditions, a skidding vehicle will actually pick up speed. It will NEVER slow as quickly as it would if traction was maintained.
