I much prefer LibreOffice. OpenOffice fell behind during the hiatus when a majority of their development team quit to form LibreOffice. LibreOffice has a big headstart on OO and a more active development team. Plus, they can pull features and bug fixes from OpenOffice while the OpenOffice team can't pull from LibreOffice due to licensing.

As you can see from the earlier child posts, opinions differ!

Using yum localinstall, I installed LO4.1 and oOo4.0 on a CentOS based desktop last night along with the native LO3.4 install. At present, I'm finding oOo has scrolling issues (nvidia graphics, proprietary drivers) and the 'use hardware acceleration' option is un-ticked and greyed out on installation. LO4.1 has the option ticked and editable on installation.

LibreOffice works on multiple versions at the same time. So 4.1.0 is just out, that'll be advertised as "potentially buggy" (forgot what name they gave it). Then they will still continue to release new updates for 4.0.x and IIRC also the version before that.

So suggest LibreOffice, as you can choose what kind of stability guarantee is good for you.

I've used both, but I stuck with Apache Openoffice because it's usually given me less grief than Libreoffice, it also integrates better with OSX than Libreoffice does.