Pros & cons of having a seperate server for MySQL?

So I am planning to move my MariaDB service over to a separate instance as opposed to my current setup with all the services in one server. I am not entirely sure about the pros and cons and a total noob when it comes to server management. :D
This site is running a separate MySQL server and Webserver. The main reason was the resource allocation for price. You actually get slightly more RAM, and an additional CPU core running 2 instances, rather than a single VPS.

An additional factor to consider, is the network connectivity between the two instances. Any latency over that will be added to every database call made.
That's what I am thinking: having a separate server means MySQL can have all the available resources for itself :D

So it's okay to go for this setup if I can get a really low latency between the server?

What are your thoughts on the TCP overhead?