I only ever use private browsing mode. Firefox delete my history, cookies and cache every time I close my browser.

So unless Google have started to do browser fingerprinting, which I don't think they have, that shouldn't be the answer. At some level I believe that Google is just better at understanding my request, regardless of how poorly I formulated it, while DuckDuckGo just returns pages where some of the word match. Given that I don't know how any of the two search engines work I may be completely of.