Hi David,
Great question!
It depends on your website and it's content. If the website is not to complicated then you can use the built in transfer tool located in WHM:
WHM has a built-in feature for migrating accounts from one WHM/cPanel installation to another. This great feature takes a lot of the guess work out of migrating websites by migrating all files, configurations, websites, images, and databases with very limited interaction.
However keep in mind that in order to utilize this tool you will need root access on your WHM account for the server that you are transferring to. Another thing to keep in mind is that you can also always ask your provider to transfer your websites and content for you. Many do not charge for this.
Let me know if you have any questions about this and the tool. Happy to help!
