Perhaps I'm the only one, but I find the Douay Rheims a bit archaic so that my younger children have a hard time understanding it. Yes, everyone might jump all over me that my children just must be "dumb". Think what you want, but my younger kids don't understand what it's saying.
I like reading the Latin Vulgate and sometimes the Greek New Testament. They're actually both very simple to read for anyone who's studied Latin and Greek. And I believe it's precisely what Our Lord intended -- simple but extremely profound. Our Lord spoke so simply and yet so deeply; He didn't need to write 50 paragraphs with distinctions. In two paragraphs He could say more than what's in the entire contents of the Summa. But then He's God.
As far as English, I kindof actually like Knox.
I don't disagree that the Douay is less accessible to most, but the OP's question was not which Bible one
recommends, but which Bible is "most traditional."
Difficult or not, there's no question that is the Vulgate, followed by either the Douay or Challoner revisions (depending on what one thinks of Challoners revisions)