Nike is more consistent than Adidas and more recognizable. I mean I didn't even know how to spell Addidas, I mean Adidas.
Nike has survived the times but Adidas has been linked to a very specific time period in my mind. The Run DMC years of rap and the early to mid 90s. Its popularity died down from then.
Nike has better ads and is more recognizable because of its athletes and because of that it is more recognizable to the masses. It also has a more iconic logo.