I've been using DuckDuckGo as my default search engine for about a month now, both at work and at home. It's been enlightening, as it's focused my thoughts about how I use search engines in my day-to-day use of the Internet.
I lean on search a lot. I'm a generalist in my day-to-day work, which means being able to recall a lot of specific information about a lot of disparate topics rapidly and accurately. The human brain just isn't built for that, beyond a certain point (you have the details of what you've most recently been working with readily at hand, but it's unrealistic to expect that you'll have the details of everything you've ever worked with in your hot cache, unless remembering things is what you do for a living).
Luckily, I have nearly the entire corpus of human knowledge at my fingertips, assuming I can convince the gatekeepers (search engines) to offer it up to me. I had always thought about search as a fairly nebulous thing; I want to know something, so I search for it. Since switching my default search engine, I've realised that, depending on what it is I'm trying to accomplish with a search, the mechanics needed to satisfy it seem to be radically different.
First, I use search as knowledge augmentation: I know the domain I'm searching within, and am using search as instant recall for specifics. This is typically the case when I'm programming or dealing with system administration tasks: I know that the algorithm, API, or command argument I'm searching for exists, I probably know a few details about it, but I need to know a specific item (that I've likely seen before).
DDG is incredible for this type of activity; it's pre-seeded with structured information that informs searches of this type, from their bang syntax, to the zero-click box at the top of the screen. They also seem to filter aggressively on the results, so you typically get a very limited set of answers, all relevant. So far, this has been a huge productivity win for me when I'm looking for information like this.
The second way I use search is exploratory: learning about a new field, refreshing my memory on a skill I haven't used in a long time, or seeing what others have done when I'm trying something new. Sometimes, this ends up looking a lot like the first style; it might be "new to me", but not at all new to the rest of the world. However, the more obscure my interest becomes, the less appropriate curated and filtered results become. These tend to be deep dives into a topic, requiring a significant investment of time.
I'm looking for "long tail" results here; an obscure post on a Chinese blog about a particular microcontroller that I have to feed through Google Translate, a mailing list post about a performance experiment someone ran with an old piece of hardware, that kind of thing. Sometimes, I'm happy to simply find someone I can contact and ask directly. It's these long-tail results that Google is simply unmatched on, in my experience, and you can't take shortcuts to get here: you have to do the hard work of scouring everything you can find, no matter how useless it might seem, and indexing it effectively.
This revelation has actually improved my productivity significantly: when I become aware that I'm researching, rather than augmenting, I scroll to the top of the DDG screen and stick a "!g" at the beginning of the search phrase (which redirects me to Google). Since using search for rapid augmentation (with knowledge that DDG seems to have solid coverage of) is my typical use case, leaving DDG as my primary makes sense for me.
Going a bit further, it clearly indicates to me that there's room for competition in this space. These are just two workflows that fell out naturally for me without putting much thought into it; I suspect there's plenty of opportunity to further differentiate here, targeting the unique ways people interact with search, rather than trying to "be the next Google".