With some gross overvaluation, I am going to call my comments 'tuppence 'orth of' and present them below, if I may:1. You have a much better command of English than I do of Japanese.
2. you have a much better command of English than I have of Japanese.
One fundamental feature of English grammar is providing the means of referring back to an expression without repeating it. This is achieved by means of pro-forms. In #1, 'have a command' is substituted by the pro-form 'do'. 'have' carries stative sense. With stative senses of 'have', as is the case in your sentences, 'have' may be handled as an operator in formal style in BrE, which means the pro-form 'have' is used. In informal style, the pro-form 'do' is preferred.
To recap, both your sentences are fine; #2 is more formal. AmE prefers #1.