I paid for both for close to half a year to see which one I wanted to keep. I decided to drop Perplexity in favor of Kagi, because Perplexity felt like it was trying to position / portray itself as a supernatural-esque Source of Truth, where as Kagi does a better job at letting you use the tools how you want.

Perplexity is also much less flexible than Kagi Assistant. The most customization you can do on Perplexity is answer a few questions about yourself, and hope that the info you add is injected into relevant prompts (spoiler alert: hope isn't very powerful here). With Kagi, I created a lens about a year ago to filter search results down to sources I find useful relating to GNU Guix, which I use for my machines. When Kagi Assistant rolled out (I pay for Ultimate, so I have had this a while) I made an Assistant that only pulls search results from my GNU Guix lens. The practical comparison here between Kagi and Perplexity is that I can go to Kagi and search "!guixc How do I install nginx?" (or simply ask the question in the Assistant interface; the bang will bring me there from search) and I will get back the answer I want. I added info that I use GNU Guix on my Perplexity profile, and there is not a chance that my question would have been answered within the context of GNU Guix as I wanted.

Perplexity is cool, but I found Kagi to simply be more useful.