Bruce Byfield summarizes the main reasons to choose, or switch to, LibreOffice instead of OpenOffice, in his article OpenOffice: A Project in Search of an Exit Strategy.
Bruce writes, “I keep asking myself what OpenOffice can do that LibreOffice cannot do better, and I keep coming up blank… LibreOffice has always held every advantage. Whatever the ins and out of the LibreOffice fork in 2010, the majority of OpenOffice.org contributors forked with it, including many of the most ambitious and thoughtful developers.
For more details, see this article in Ars Technica: OpenOffice, after years of neglect, could shut down.
Also, Contemplating the possible retirement of Apache OpenOffice.