I am the creator of Favimon!
The answers so far are more or less correct, it's mostly a site's position in the database that determines how high its stats are. The database is loosely organized - really popular websites are at the top, but otherwise it's basically a big list of websites that I am constantly adding to. Also, certain classes have their stats bumped in certain ways.
The actions each favimon has are based on the favimon's classes. But they are also randomized each time a favimon appears, so even though a site has a really powerful attack action, you might not get that action each time you play.
You can also randomly find favimon with special classes, like 'shiny', which have their stats bumped.
It's messy and esoteric, but it mostly works. In the future I may come up with something more sophisticated.
Thanks for your interest in my game!