LibreOffice is original OO, in terms of continuity of development, more so than AOO is.
And another one to some extent: oOo uses its own font rendering, the LO team (I gather) moved over to using libraries (harfbuzz) available in host OS for font rendering. I seem to have better results on former under some circumstances.
I have not had any round-trip editing problems flitting between the two under Linuxen of various kinds.
I didnt know this but at a more general level I am reluctant to "upgrade" what's already working fine due to this very fiddling with new stuff which is a common failing of the FOSS model in my experience (people wanting to add shiny things instead of making existing stuff better - Firefox, GNOME etc). This is one of the main reasons I did not migrate to LO.
Are you using a distro from 2010? Because I believe most of the major Linux distros include LIbreOffice as part of the default install.
I just checked - the latest I use is centos 7.1 which does have libreoffice already installed, however my daily machine is older and I had to install OO manually there.
Wasn't OpenOffice own by Sunacle at some point?
I think that's when a lot of users moves to LibreOffice.