Potato skins are more nutrient-dense, but are also where all the toxins reside. A few less nutrients for a lot less toxins = don't eat the skins IMO. The only reason to eat potato skins are, well, you WANT potato skins as a snack. If you're not specifically craving them, cut them off because there's no reason to eat them.
Eating starch for nutrition is a terrible idea, anyway. Starches lack nutrient density, so people who make their dietary staples sweet potatoes, white potatoes, white rice or grains in general aren't doing something smart. Even the most nutritious starches are less nutrient dense than some of the least nutritious vegetables. You should be eating starches as a low-toxin source of complex carbohydrate if you need carbs in your diet. If you don't do carbs, there's no need to eat starch since you can be filling the calories with more nutrient dense foods.