So is the slavery better or worse when it's "white"?
I am not sure how that term "white slavery" originated, sir; I believe it was first used in the Mann Act of about a hundred years ago, an act which prohibited the importation of women from one state to another, so as to profit from their prostitution.
Since this was about a hundred years ago, and there were still many living who had memories of slavery, perhaps the appellation "white" was used to differentiate; "black slavery" (thank God) having been abolished about forty years before, but still in the national consciousness.