In my opinion: you're clipping content + structure, and not just something like images/text. So you get to preserve the original layout, links, etc, which is a huge benefit.

You can also have things private and/or shared with a select group of people, which is what I usually do.

For example, a common use case I've found is that I'll clip something from Gilt/other signup required sites, to show someone a deal they might be interested in, but they don't want to sign up just to look at it. If they like it, they end up signing up.