Moving from Rackspace cloud files to Amazon S3
I would recommend not drag-n-dropping inside Craft. It might end up being very intense indeed, and break down in multiple ways.

A better way would be to download the media locally, replicating the folder structure and files in the S3 bucket, and then manually changing the source id of the Asset / Folders in question in the database.

For concurrent uploading, take a look at s4cmd.