Use rsync once you have set up the domain on the new server. The only reason I can think of that rsync may not be the best option, is if it's a Windows server.
If you use the control panel backup software, you are going to need at least DOUBLE the disk space to the data you want to backup and move, on both the old and new servers! The problem with this option, is that most cloud based VPSes do not support shrinking the storage once you are finished with the migration, so you end up paying for disk space you are not using ...