Here's the quickest answer: https://help.kagi.com/kagi/why-kagi/kagi-vs-competition.html#kagi-vs-duckduckgo

There are a ton of features that Kagi has and other search engines (including DDG) don't, you can see the range of these in the features list on the sidebar of the above link, especially the many detailed ways you can customize your search results: https://help.kagi.com/kagi/features/website-info-personalized-results.html 

Kagi Search also actively downranks sites with lots of ads and trackers in the results and promotes sites with little or no advertising, shows if a site is paywalled from the results page before you click, allows you to filter out AI generated images in image search, and much more.

The best way to see the real difference is trying it for yourself - explore the settings and personalizations, see how far you can go with Kagi Search vs. others in the market, all without ads poisoning your experience.  

 I like advertising. I am a lazy leech who cannot justify paying for all of the online services I choose to depend on, or the content I choose to consume.

Advertising is a way to give back to those I choose to associate with, and more importantly, it is probably the way to give back that has the lowest possible barrier of entry to me.

Advertisements are just what I deserve, and what the creators deserve. I have been aware of the option to disable ads in Duckduckgo for quite a while now, but I refuse to take advantage of that option. It makes me sad and frustrated that Kagi does not have the option to pay through ads.