You are mistaken. Even with a very crude grasp of the language, anyone with an ear can discern the superior actor.
Both actors could be speaking gibberish and it wouldn't make a difference, one will be doing it better than the other. Perhaps both actors are strong in their own way, but one will always be better suited for the character.
So the question is, which actor makes for a more credible, or real/authentic Chihiro? I would say hands down, in this case, it's Rumi Hiiragi. Mr. Miyazaki picked her because he felt she was the right match for the character he had in mind, and he guided her performance to where he wanted it to go. I wouldn't want to place that work and those decisions in the hands of anybody else.