Not OP, but:
1. Older results. DDG's recent (<~5 year) results are pretty good. Going older than that for online content, not so much.
2. Books and journals. Google Books, Google Scholar, and Google Ngram Viewer are phenomenally useful tools, no doubt about it. There's no single resource which can substitute for them. Worldcat (library search) is good, if you've got access to various search databases (usually via an academic library) that's useful, and content access itself is possible (with questionable legality) via Sci-Hub and LibGen. The Internet Archive has less content, but greater legality.
3. Specific technical queries are generally less well answered by DDG, but easier to direct (via bang queries) to the appropriate source. StackExchange, Debian, Debian packages, Ubuntu, Microsoft KB, etc., are (I think) all covered. The ease of filtering from a general case to a specialised search is a real win.
4. Date-bound searches. I very frequently want to look for something between specific dates.
5. Less-prominent content. I use various sites (Ello, Reddit) as filing cabinets of a sort, and being able to search my own posts there is useful. Reddit's post search is good, Ello's not so much. DDG doesn't index (or retain) Ello results well.