But to my first question, big changes, I mean more on a personal level; What will change for me, like do I need to look out for certain things like software updates, the state of the server and things like that. I'm a fast learner but if it comes to it, I prefer to keep everything as simple as possible. Like I don't care to know HOW a car drives; just as long as it's going forward, I'm fine with it.
VPS and dedicated environments have a lot of similarities. Software upgrades, advanced setup and server stability are responsibilities of server owner in both VPS or dedicated environments. Server control panel like cPanel or Plesk is a good help with first two. To help with the last, Lunarpages offers a number of management addons which include monitoring of your server by Lunarpages staff for important services and acting, if they stop working.
I'd like also to correct Catalin. It appears you don't have cPanel on your VPS and more than likely use Plesk. So to use data migration for free, you will need to choose the Plesk control panel for your dedicated server