That was an important character development point. She was at another crossroads, she could choose to be no-one, an assassin for hire, but she stayed true to who she's always been, someone with a (at times misguided/simplistic?) sense of justice who will kill for a cause and/or vengeance. She's not as physically skilled as the waif, she was never going to go out and win a bunch of hand to hand combats based on strength. In the end she proved more clever, a better read of character/tendencies/motivations/environment, which is more important in most cases for the kind of work she'll be doing. Those are the lessons she's learned and skills she's developed along the way from Sorel and mostly Jaquen. She didn't beat the waif by playing the waif's game, she beat the waif on Arya's terms.