Well, it's simple.
Socket is a file based communication, and you can't access the socket from another machine.
On the other hand, ports are open to the world (depends on configuration) and you can access the mysql from other machine using host+port combination.
Also, as much I understand sockets, they are just combination of host+port, just in the file format. So, I don't see any clear benefit in using any of them (as much my knowledge goes).
Though I personally prefer using host+port, as my code becomes more flexible, as I can move it to the other machine, without changing much.
Copy pasting from some old post:
Unix sockets are a little bit faster as you don't have the
tcp-overhead. If you realize this performance loss is a question of
server load. If you don't have very high server load you won't
recognize it.
If you use Jails (FreeBSD) or some other virtualisation technology to
separate the e.g. MySQL-Server from the Webserver, you often use the
tcp/ip setup instead of sockets. The firewall rules need to restrict
the access though.
You need to find out if your system is under heavy load so that a
socket is a must or you can focus on a nice system design (separating
services), then a tcp/ip solution would be better.
So make a long answer short:
Yes, there is a performance difference, sockets are faster. If you are
not suffering high server load, just choose what fits better to your
system's design.