Can't say much in regards to perplexity, but I find kagi's index to be quite nice. Especially if you find fortune forum posts helpful (which I do as a software dev). It's paid only, so there's no advertising incentive to the company and also a ton of configuration. I search a lot, so I went with the 10 dollar plan. 5 bucks gets you 300 searches a month, 10 is unlimited plus access to their LLM which documents information sources like perplexity.
Personally, I found perplexity to be quite annoying with the more ai focused UI and trying to learn your interests. Kagi is a search engine first plus some other features they're developing.
As far as I know, Kagi doesn't have their own index. They use a mix of google and brave's results (maybe some other search engines too?), and then sort their results to give "better" ordered results.
Yeah, from my experience I believe Kagi’s results are like 90%+ pulled from Brave’s search index. I like the concept of Kagi, but I prefer SearXNG as a search aggregator.