FTP is a much older and more widely used protocol and it's tied (in our system) directly to users you create. Only one ftp login can be used to access a specific set of files.
WebDAV goes over HTTP (and thus port 80) and is sometimes better for getting through an aggressive corporate firewall. It also allows for more collaborative editing because it supports file locking and multiple users accessing the same files. The big downside of WebDAV in our system is the files can ONLY be accessed through WebDAV and can't be accessed any other way. That's due to the way our shared servers are set up (mostly to protect users from each other) and the way WebDAV has to work.
In a dedicated server environment, you could use WebDAV more fully. But in a dedicated server you could also open up FTP more for collaboration that way.
They both provide some of the same functionality and can be used for similar things. For general use, you will probably find FTP to be what you want to use.
- DreamHost Head Honcho/Founder