LiveView tries to replicate the architecture of a native app toolkit and slap a network boundary in the middle of it, whereas htmx tries to keep the programming model of Web 1.0 apps while radically expanding the user experience possibilities
HTMx is more about simplicity - an easy alternative to AJAX that doesn't require a full-blown front-end framework. It isn't really designed for optimized real-time communication and long-running connections, but you could probably use it for that if you wanted.
With LiveView, it seems to be just sending application state up and down the websocket wire, does HTMx not do this as well if it was setup that way with WS?
it tries to extend HTML as a hypermedia, which makes it more general (it can be used with any backend that produces HTML) but also more work to achieve things that, in live view, work magically
htmx is just html++: any element can make any sort of HTTP request (GET, DELETE, etc.) based on any event and replace any other element in the DOM.
much simpler and "dumb" when compared w/ liveview, with no particular server-side implementation implied