This debate has recently come up where I work. In my experience over the past 30 years in CAD/CAM, we have always worked locally and later copied our projects to a network for backup. Of course these have been companies with just a handful of designers who did not collaborate on projects and need immediate access to the latest version of anothers files.
At my current job, we just had a rather unpleasant experience of building a down-level weldment (2 weeks fabrication work down the drain) because the revision was not successfully copied to the server from a local drive.
What methodology do the rest of you apply and why?