Let me add to the excellent explanations of qubit just encouraging comments, experienced based:
I installed about 6 month ago LibO parallel to MS Office 2003 on my XP / SP2 old PC without any special considerations. After the installation I opened Tool/Options and made here and there a change to the default settings and just started working with LibO (with experience I changed a few more). I tested LibO for about 2 month parallel to MSO 2003. There are things, which I found better in MSO but there are more things I found better in LibO. Thus, my new PC (originally W7 but downgrade on purpose to XP /SP3) contains only LibO and no MSO anymore.
Compatibility is not really 100%. docx or doc format? I tend to say doc is better compatible but I never made a real comparison. Reason is that I converted to LibO because I like it better and tackle the problem of MSO compatibility on a case by case basis.
Should you use Writer often, I am pretty sure you will like it soon better than Word. I found that Writer is much easier to be used. Especially the Styles in LibO are much better structured and easier to be used. I never understood the MSO Styles really and they always caused me head aches.
And there is the bug report and enhancement request possibility. In LibO I can see what happens to my bug reports and enhancement requests and sometimes I get even questions back. With MSO I don’t know about such a possibility.
So, go ahead and install LibO (I am running 3.6.4.3) still in this year and have a great start with it in the next year, which starts next week.
And if you have a question, you know already where to ask.