I would prefer to have content on my site

Yes, it's not really a case of either/or, but you really want to have something newsworthy to justify the release.

Is there something unique or buzz worthy that the press would like to publish and that people should know about?

It could be something simple like a new officer at a company or even a special event with prizes and contests.

A press release isn't going to be written the same way you would write for your website so there shouldn't be a conflict.  In this case, you should write a separate press release.  You can't just take one of your articles and turn it into a PR; that's not how it works.