Enterprise grade file sharing

Check out AjaXplorer. Dead bang simple for end users, nothing more than LAMP to run.

FTP

One word: WebDAV (if you really want it to be web based, else you can try scp/sftp with private key and forced commands)

I'd look at either Accellion or Allardsoft File Transfer, very broadly similar but vastly different pricing.

Both are VM's so they don't strictly fit your "Must run on Linux" criteria, but they do "just work" and are focussed on sending and receiving files.

One key thing as well, they are both "self service", no setting up FTP users or having pissed users calling because no-one was there in IT when they needed to send a 5gb file at the last minute on a Friday.