Nike is losing the fashion battle to Japan's Asics, with consumers shifting from Air Jordans to Asics's chunky dad sneakers. That is a potentially fraught win for Asics and a quiet victory for Nike.

Running's growing popularity has helped catapult shares in Asics, a favorite among runners. It is by far the top-performing sneaker stock, having grown more than fourfold over the past three years.

Nike cruised on popular lifestyle sneakers—Air Jordan 1s, Air Force 1s and Dunks—for too long and fell behind on running. It is the worst-performing sneaker stock, declining 62% over the same period. Losses to Asics in fashion are offset by gains in the more durable performance category.