I have not used WS_FTP, but any FTP program will let you upload and download from FTP sites. I have not needed to do any site to site transfers, though, so I am not sure how common that feature is in current FTP programs (it shouldn't be too hard to find if it is needed... and supported by both webhosts).

A couple freeware programs I've seen recommended are FileZilla and WinSCP. Personally I've used LeechFTP (which is getting a little long in the tooth), but mostly stick to the FTP function built into an older version of the PowerDesk file manager (a freeware, but lesser featured alternative is FreeCommander).