Depending on your bow's geometry, the double line may reduce swing on the mooring, or so I've been told. My bow geometry doesn't look like there's much effect, BUT I do now use the double line anyway after getting screwed over by the single line once.
in a crowded mooring field the week before July 4. Tied on with a single line, as conditions were very mild and I honestly didn't even consider the 2-line setup. Later in the day, the mild conditions turned to a perfect flat calm. The moorings were "designed" to accommodate boats up to 55 feet, meaning there were precisely 55 feet from one ball to the next. My 43 feet and a neighbor's 45 feet meant their stern was routinely within spitting distance of my bow. In the flat calm, the boats no longer pointed nicely parallel to each other through the mooring field. One unlucky eddy swung my neighbor's boat about 140 degrees different from my heading, and bang! His dinghy
(on davits), swung into my solar
array and bent the hell out of them.
Don't get me wrong, having the double-line would not by any stretch of the imagination prevented this incident. However, the mooring operator's website apparently had fine print somewhere stating this was required. Because I did not have the double line, the mooring operator managed to escape paying for my damage, despite a mooring field that was clearly packed too tightly...
You live and you learn, and I repaired the array myself for a hundred bucks or so, and now I avoid mooring fields if they are too full. But I do run a 2-line bridle just in case it helps me in any future insurance