One button: Add to Any is a single-button solution that saves you precious page space and from cluttering your pages with a bunch of Add to [Service] buttons.
One click: Users of Add to Any typically save their services so that any Add to Any button, including the one on your page, is a one-click link to the service(s) they use.
For RSS feeds: Your feed becomes exposed to the widest possible audience since Add to Any includes every user's feed reader.
For pages: The Add to Any button/link reminds your visitors to bookmark your pages and links to every online bookmark manager.