Your example seems to have nothing to do with carried interest. There's a single investor; no investment manager. The question around carried interest is whether certain types of income earned by investment managers should be classified as labor or capital income, whereas you have one person with labor income and one person with capital income, and are asking who should be taxed more heavily.

In my comment "I" am the investor and "you" are the investment manager.

I'm sorry if that was unclear.