It looks like the PHP version uses AJAX requests instead, but most importantly it doesn't persist any state on the server continuously. And then it looks like client requests send the current state, as well as checksums etc. to keep it secure. Then the server spins up a new instance of the class, hydrates it with the current state, runs the requested operation and returns the dom patch.
It looks like LiveView has much smaller requests/responses and both client and server do much less work. But the tradeoff of that is that you have lots of Elixir processes, which I guess pretty much only works with something like the BEAM. And you have to be careful about memory because those processes all hold a client's state. If you want to display a page of database results then that's fine but you'll want to clear them from the state instead of keeping them in memory for as long as the user is on the page. And of course then you're going to lose some performance if you need that data again for a future operation by the client. The Livewire approach doesn't force you to think about that, you don't have the choice to hold the state in memory.