I believe CPanel is most secure in terms of security. The webmail service is quite secure and i've never had problems using it. Also i think CPanel uses Thrid-party webmail services like Squirrel mail, Horde mail and Roundcube. If you could find stuff on how to secure these, you'll be pretty much good.
CPanel has also suggested this :
Upgrade your mail to maildir format
via : http://www.cpanel.net/2007/06/10-tip...re-secure.html
Maildir format adds extra security and speed to your mail system. Newer installs use maildir by default.
If you’re running an older copy of cPanel, you’ll probably want to upgrade using /scripts/convert2maildir.
Make sure to back up your current mail before converting to maildir, this can be done within /scripts/convert2maildir.
If you see maildir is enabled when running /scripts/convert2maildir, you are already using maildir, and will not need to convert.