I'd follow LibreOffice, it's more feature rich, plus LibreOffice is licensed under the Mozilla Public License and LGPL3, which means OpenOffice won't be able to use all the progress LibreOffice has made. I have a feeling OpenOffice has a very short lifespan at this point. I am however in no way an expert on either of the two, this is just what I have read over the months.
Can LibreOffice use the improvements to OpenOffice? If so, it seems like the relationship could become quite one sided with LO able to pull in all the fixes to OO and use that to move further ahead, but with OO unable to re-use any of the LO work.
OO uses the Apache License, which would allow LO to pull any change it wants. Of course it doesn't work the other way around, because LO's licenses are more copyleft. So you're right, it could get quite one-sided.
For the past year LibreOffice has been the one worth following because OpenOffice was put on hold after the Sun acquisition, then shifted to Apache where it has now been resurrected.
My view would be that it is well worth seeing what Apache do with this, however Libre currently seems to have more active development (although I could be completely wrong as I don't know what sort of resources Apache have been throwing at this).
Given they are both free, it would seem like a good idea to pick one for day to day use, but follow both closely, much like the situation with the browser wars.