Hi 
I wouldn't say that either is "best". It entirely depends on situations and specific requirements.
Both covers the large middle ground really well but each has it's niche areas where it's marginally better than the other.
Apache OpenOffice develops more slowly so known bugs stay longer and fewer new surprises occur. So, once you find a bug there you can be fairly sure it will be in the next several releases. That means AOO is "more stable". One advantage with that is that if you know a work-around for some annoyance then that keeps working too.
LO just fixes a lot of those problems but doing so might sometimes create new ones (which also then largely get fixed). However, that does mean there might be some surprises. To get around that LO actively develops 2 branches. One "more stable" and the other with more new features.
In both the 3rd digit in the version number is roughly the same as the "Service Pack" number in MS software, except that we go a lot higher.
So i have most machines at work on a x.x.5 (ish) and wont install anything earlier than a x.x.3. My own 2 work machines keep leapfrogging each other but soemtimes return to a previous version or to the one installed on the other machines. I keep meaning to test-drive the very earliest releases of new branches but rarely do and even if i do never find any problems because i just don't need anything even vaguely advanced.
My dad now lives on a boat which is often out of range of "the internet" so i would probably give him AOO, or an LO version such as "higher than x.x.5"
Regards from
Tom 