I haven't found Kagi's results to be significantly better than Google's results, but unlike DDG they're not hugely worse than Google. It's all the extra stuff that makes me want to use Kagi instead of Google:
* Ability to banish sites from results forever. E.g. I never want to see the Concordia Lutheran High School's website when I search for things in the Common Lisp HyperSpec with clhs.
* Ability to weight sites higher. E.g. there are two mirrors of the Common Lisp HyperSpec that appear in results, one at http://clhs.lisp.se and one at http://www.lispworks.com/documentation/HyperSpec/. The lisp.se mirror is hilariously slow for me (5-10 seconds to load) while the lispworks one is instant. Google always ranks lisp.se first which tricks me into clicking it and wasting my time. Kagi lets me weight that site lower so the lispworks site comes first. Banishing lisp.se would also work, but just upweighting it means I can still find it if the other mirror ever goes down or something.
* I reported a minor bug to Kagi and they fixed it within a few days. I doubt that would happen with Google.
* Supports DDG-style bang queries, which I use occasionally.
* No goddamn ads/tracking (I use uBlock Origin, but it's the principle of the thing). I've almost entirely de-Googled my life at this point (Youtube is the only holdout for me).
So it's not that it gives better results than Google, it's that the results aren't any worse and the extra quality-of-life features are really nice.