FilleZilla, WinSCP, either are perfectly fine, they are just as secure as any other FTP/SCP program out there. The security is through which protocol you use. SFTP, SCP, FTP, etc.
I personally use SCP (Secure Copy) which is SSH based, so unless you have Shell access, it won't be an option. The thing I like about that process, is I can use a public/private key instead of a password. You can read more about that at http://winscp.net/eng/docs/guides