DriveHQ Online Backup has a feature called "Migrate". You can find it in the Manage Tasks screen of DriveHQ Online Backup.
The first step of migrating a task needs to download all your files to the new PC, which could take a very long time. However, if the same files are already availabe in the same folders on your new PC, then download will be skipped.
DriveHQ's new Magic Upload technology can make uploading extremely fast if you are uploading the same files that have been uploaded before and you have not deleted your online copy. So it is strongly NOT recommended to delete files if they will be uploaded again.