It depends on the content of each essay, but I think it's always good if you can cut down on what you're asking the admissions office to read. If you cover your diversity factors in your PS, you don't need to write a separate DS.
Real quick- does an immigrant of Cuban/ Russian background quality as diversity? I attached a diversity statement underlining why my background means so much.
I just wonder if the Russian portion of my background kind of kills my diversity.
Definitely have a question about Personal statements vs. Diversity statements and if I should write both if my Personal Statement sort of seems to accomplish what I'd want in a DS.