WebDAV and security

Our company has a need to securely transfer sensitive files and we currently use FTP but that is no longer suffice. It has to be secured. So, I have come up with using WebDAV and a SSL cert but I am getting some resistance because of WebDAV’s bad security rap.

My question is, does anyone else use WebDAV for this reason? Is it safe? Have you had any security issues with WebDAV? Do you use any other methods to help secure WebDAV (such as deep packet filtering)?

The answer that gives me the most helpful info and insight on WebDAV gets the points.