GoDaddy is known for being a horrible host. They are a great domain registrar, but lack in the hosting department. That goes for pretty much all domain registrars.
Last I heard, GoDaddy uses a proprietary control panel, so whether or not you can just transfer your sites without losing things, I'm not sure. Your best bet is probably going to be to back up all the databases manually, then restore those on the new host, and re-upload the rest of the files manually via FTP.