Both have greatly disappointed me by not even trying when I apply quotes to more than two words. Can't say I've done a deep dive comparing their privacy but I try to spread things out among search engines.
Just my experience, but DDG results are still consistently worse for me. When I do try DDG and Mojeek first, there is about a 1 in 6 chance I will need to fall back to Brave or Startpage to find what I'm after.