He's still an elite ninja and a prodigy even without the sharingan. He may have gotten the moniker for being the copy ninja and mastering 1000 jutsu (with the aid of the sharingan), but he's as skilled, famous, and feared as he is because of how resourceful he is at using the tools at his disposal. Of which he's amassed a ton, making him exceptionally versatile and well rounded.
He's not as good at genjutsu as, say, Itachi or Madara, and he's not as good at taijutsu as Guy, or as good of a strategist as Shikamaru, but he's still better at strategizing than most combat strategists, better at hand to hand combat than most hand to hand combat specialists, and has more experience than most ninjas. In the event that he encounters someone with better raw skills in one area than him, he can usually rely on his experience and his versatility to give him an advantage.
You basically have to be a master of some specialty to beat kakashi in it - and if you can out class him in one specialty, he'll outclass you in five others, and use those to beat you, instead.