Well, OpenOffice is obsolete (not sure if officially - probably, they've changed their mind about discounting it, but it was announced some time ago), and LibreOffice is both code, contributors, and ideologically-wise continuation of OpenOffice. LibreOffice started after Oracle actively presented their hostility against FOSS at all, and autocratic (as opposed to meritocratic) stance on accepting/declining OpenOffice code contributions.

Long Story short, 99,99% of active OpenOffice code contributors started "fork", and things like GoOO also headed in this direction. freed of limitations from bounds with DamnBigCompany (sounds familiar? ), LibreOffice development got epic momentum and it's flourishing.

Trivia: LibreOffice was meant to be temporary name, but Oracle refused to grant name to newly formed foundation.
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All after all, i strongly recommend every OO user upgrading to LibreOffice.

/Estel