Like many I've run numerous online services both for my immediate family and also public "services" like this blog! (lol). Its almost always the case that a VPS comes with some kind of web based control panel, while these are convenient they do tend to isolate you from the nuts and bolts of the "engine". Indeed when backing up my emails I ended up giving up trying to find the files and resorted to hoovering them up through the imap interface... With some control panels having multiple server configurations can result in rather confusing multiple file-systems, especially after running for a few (or more!) years with different domain names coming and going... Faced with a situation where the current vendor was ignoring support tickets about upgrading an OS that had fallen out of long term support, a friend and I decided we should take advantage of a package offering much better value and more flexibility. Actually cheap enough that we could each get our own separate server at less than half the price of sharing a VPS!
OpenVZ has its own unique set of technical pros and cons, but one not to overlook at the moment is its cost value. For me by far the biggest technical pro, will probably sound like a con for some people, after installing an OpenVZ template in a container you typically end up with only just enough OS to support an SSH session and nothing more... While some control panel install scripts will even install everything they need (usually a fairly typical (L)AMP stack) and indeed when first exploring the service that is actually what I tried, I soon noticed that no matter how good a control panel, you are often left with some interesting "edits" in config files - and indeed for anything less than a vanilla configuration you will probably have to get your hand dirty with some actual config files anyway...