I believe both are used for customer facing applications. However, I am not sure about b2c at scale. You could argue that Hey.com is b2c.
In this case, the main advantage is that scaling is stateless, so your application servers just have to be able to deal with more traffic. There is nothing more to it.
As for Phoenix LiveView, it has both advantage and disadvantage of being stateful (something as using Action Cable). You now have to be scaling web sockets, but you save on authenticating the request (the request is lighter).
Even if LiveView is stateful, it's done on the platform which is optimized exactly for this purpose.
In both approaches, you also have to take into account that server latency might be a deal breaker for you.