I also have the same experience where kagi doesn't find something I think it should, so I go try google. Holy hell is google bad. Shockingly bad. I genuinely can't believe how bad it is now compared to 10 years ago.
Kagi is designed to show you what you ask for, and not for showing you the ads you're most likely to fall for. It simply takes your query and returns results matching it. That's really it. It's sad that "does what you ask" is a defining feature, but that's what kagi is.
They have advanced features like "lenses" that bias your results toward a specific topic like programming, research, forums. It also lets you add weight to certain domains. For example, I have Pinterest and Facebook totally blacklisted, and some small sites boosted in my results.
They also support advanced query syntax with double quotes, +/-, and other operators.
Which is to say, kagi is the standard for "search engine that works". Nobody else sells a search engine that just works and does what you tell it to, which is literally all I want out of a search engine. It's mundane and unsexy, but it works, it doesn't advertise at me, and it lets me get my work done faster.
- Especially if you feel the need to use doublequotes.