Use either of the neutral-grip handles to put your arms in a stronger position. While you'll be able to use more weight, remember that your arms bear some of that extra weight. When you use the narrow grip, your chest also does some of the work. Keep in mind the extra muscle involvement, and don't make these neutral-grip movements the only back exercises you do.
Just like it sounds: one hand over the bar, one under. The only advantage is the spice of variety.