Apparently a great deal, in the eyes of Oracle and the OpenOffice team.
It seems the OpenOffice team - now the LibreOffice team - have had some kind of falling out, and the resulting schism means that if you'd like to best of OpenOffice, you'll want to move to LibreOffice.
Most users can find a download for it at their download page:
Linux users won't always have their distro catered to, but this is a common occurance. In due time, it should be as widely available as the older OpenOffice was.
So we won't talk about that.
What we'll talk about is the differences, specifically in the naming.
Naturally, OpenOffice is now LibreOffice. This brings other side-effects though. The binary name is no longer soffice, but libreoffice - make note, those of you who use custom menus. You'll need to update them.
This also means that users of Cairo-Dock (and potentially other docks) will need to alter their launcher.
Now, for other docks you may have to do a little figuring out, but for Cairo-Dock, here's how to alter an OpenOffice Writer launcher to serve the same purpose with the new suite.
Grab your launcher settings, and set the command to launch to this:
If you'd prefer it to launch without starting Writer, Calc or any other, simply remove '-writer', or change it to the part of your choice.
Now, while your Launcher will work in this state, if you open a document, you'll find that it won't use the launcher as it's Icon (if you have that option turned on). To fix this, open the 'Extra parameters' part of the launcher properties, and look for the part labelled 'Class of the program'. Change this to 'libreoffice' and watch as your documents all move to the launcher.
While this change may be small, it's an interesting one. I'm interested to see what's coming next for the newly rebranded LibreOffice.