Google still wins when you don't know the word/term/name etc for something and are describing it. The reason for that is mostly that every time someone searches on Google, they help make Google smarter. Effectively every time you search, the results are largely based on what someone searched for historically and what they clicked (or even subsequent searches and clicks).
e.g. "movie about kidnapped daughter" (I'm looking for the 2008 movie Taken, but have "forgotten" the name).
Google: 3rd result. Bing: 8th result. DDG: 7th result.
Why is Google 3rd and DDG/Bing 7th and 8th respectively? They likely have all indexed the Wikipedia and IMDB pages for the movie Taken. However Google likely ranks those links closer to the top because historically that's what users want when they searched for that phase.
By itself, one data point like that is extremely weak evidence; the later queries might actually have been completely unrelated. But that's a source of error that tends to disappear when averaged across a large number of different users. In the aggregate, the data can be extremely valuable. But doing that kind of analysis requires correlating multiple searches from the same user, and storing the resulting profile for a long enough period of time to do useful aggregation.
This is a search problem. I honestly don't see why DDG can't develop an AI that understands cultural and language contexts. Currently it doesn't but innovating this will take a lot of brain power, something DDG is lacking (when comparing the sheer #s of personnel focused on search).
1) Smaller index. Some stuff just seems not to be in DDG at all. Even after finding a page I'm looking for via !g, I'll go back and try to see whether I could've gotten DDG to return it with some more specific search term (even verbatim phrases from the page) with no luck.
2) Languages other than English. The Google/DDG search quality gap is much, much larger in Greek than in English, for example.
I should probably have tried more but I guess I'm too pragmatic for my own good.