Migrating drupal site from one server to other could be easy and fast task, then again if not prepared you could run into many problems and have lots of work.
One of the biggest problems you could face is that you are moving drupal site that hasn't got all the modules updated and latest core. The problem occur if you had all of this also on and "older" server, where php was 5.2 for example. What would happen is that on your new location you would probably have 5.3 php version and some modules and drupa 6 cores work ok with 5.2 but throw warnings or even errors on 5.3. So this could be a pickle for you, you would need to update all the modules and the core, but also hope that site was made "drupal way" so that updates would go without problem and data loss, if not you would have to b careful. So advice is to check this before you do and count it your working hours.