I can't speak for teens, but I climb and ski. In the past, I would have said all three were comparable brands in terms of quality. Now I find NF a bit lower quality. HH is high quality, but, IMHO, better designed for ski resorts and sailing. For backcountry sports, I like Patagonia the best.
Since you posted in Beauty and Fashion, I'm assuming you are asking more from a day-to-day winter jacket perspective. For a growing kid, I would say it does not matter. My kids wear Marmot, Eddie Bauer, and Deux par Deux while skiing...but they only ski in ski areas.