Which would be faster? More stable?

I have a client on a VPS that is starting to get traffic, I am going to move this client to their own server, BUT I will set up virtualization at the root and they will be the only VPS on the machine. This gives me some management options I do not have just installing them in the root.
HERE is the question... Should I leave their social networking site with heavy calls to the database all as one VPS, or would setting up a second mysql server on a vps in the same machine give better performance?
The script phpfox, is setup to run on multiple servers or just one.
I am thinking that the ram and processors would ultimately be required to do the same tasks split or together...

Hello,

Unless you have two separate HDD/SDDs there is no reason to split apache/php and MySQL into different virtual servers. If you have 2+ HDD/SDD then you could dedicate a disk to every single VPS and you would probably get more speed as IOs will be independent.

Anyway you might test the both installations, install two virtual servers: one with full LAMP stack and a separate server with only MySQL, and test speed, first with MySQL on the same virtual server, and then with MySQL on a separate server.

Maybe if you're looking at the way MySQL caches, and you got 2 distinct parts; it may help to have 2 MySQL setups on 1 hardware machine so each part gets their fair share of caching. But that seems a bit far fetched.