It's not necessarily one or the other but definitely skews towards the aesthetics/fashion element. That said, the best designed sneakers often rank highly on both of those dimensions. Another poster mentioned Nike's rise in running shoes. They're highly functional, often the best in the game, but also designed with enough attention to aesthetics to be seen on the foot of many executives in their day to day lives. That's good design.

To the gp's point, the single pair of UA sneakers I own are highly functional and sport-specific that only come out at the gym...but picking them out of a crowd of UA's lineup is difficult.