Before Kagi I was running self hosted Searx (technically searxng as it keeps getting forked) which is a search aggregator. It runs the same search over multiple engines then lists the results based on which ones come up the most often. I like Searx but it’s slow (takes a few seconds to retrieve all results from search engines and build the page). Kagi does the same but is very fast.
I’m not sure the search results are generally better with Kagi but it does have some great features. E.g. you can block, lower, raise, or pin certain sites. So I block all the Pinterest domains so they don’t show up in results, and I pin Wikipedia so if it’s in the results it’s always at the top.
Raise and lower just bump up or down that site’s importance.
There are also some AI things like summarising pages and one I recently discovered is you can type in a question and get a chatGPT-like response (but it’s not using chatGPT).
I think the main reason I use it is not that it’s better but that I like to support projects that are trying to do things different, I want a world to exist where a search engine can sustain itself without ads (since I’m gonna block them anyway). I’m lucky that the cost isn’t an issue for me, so I see this as a way to support the goal.
If you want to test it out, you can sign up for 100 free searches (and can then also have a look around all the customisation options), but if you’re already a pretty skilled searcher I wouldn’t expect it to be significantly better.