Clara's the only companion we regularly get to see confront the villain without the Doctor and manage to not only hold her own but succeed. Even in Deep Breath, where she's visibly shake and scared and not used to this, she wins and turns the tables on her opponent so she's interrogating him. Usually we only see companions confront the villains alone to show how out of their depth they are and need the Doctor to ultimately come in and save the day.
But Clara frequently gets to do it herself without failure, and we see her become progressively more confident (and more cocky) at it. Lots of companions get to fill-in for the Doctor when they're out of action, but Clara is still the only one that you can honestly say became her own Doctor that it was no longer a question of "What would the Doctor do?" but "What will I do?"