Real time - Which is the best way?

I'd caution against using any brand new technology especially when it comes to scaling. Until a platform is proven it's a gamble if and when support or development may stop leaving you to rewrite your application. socket.io has been around for years and isn't going anywhere any time soon. If the unlikely event occurs that you have to handle volumes like WhatsApp you'll have the resources required to make that decision.

Phoenix is built on Elixir/Erlang which has powered telecom companies since the 1980, it's not new technology at all, it's just not object oriented and is functional instead.

Addition:

I'm not saying he should use Phoenix + Elixir but he asked for what's out there and I stated so. He specifically stated "Like Facebook" so if you take it literally, I described pretty well the different scenarios. If he wants something that is very powerful, proven, tested, and has been around for a long time, then you can go with something like Elixir. If you want something that's easier and still scales well you can go with nodejs + socket.io. If you want something that probably will crash quickly, try implementing PHP websockets.

And just to add, most 3g, 4g and LTE networks in the world are powered by Erlang. It is in no way new.

Codeigniter is simply one of the tools you need to learn to be a successful developer. Always add more tools to your coding arsenal!