Surprisingly well, at least in the case of Kingsoft (the only one I've even briefly messed with that isn't Drive.)
I think assuming that LibreOffice is necessarily the more capable product is a bad assumption; there really are Android apps that outstrip their best Linux competition. An example of such an app (not a word processor, but you get the idea) is ezPDF, which beats every PDF annotator available on Linux, including that $85 USD monstrosity in the Software Center.
I got along fine as a student with Linux and OO. I don't really see the jump from that to Android as an extraordinary one.