Not really. Libre has a huge headstart in terms of features and bug-fixing and creating maintainable code, and can pull in anything that Apache changes almost as soon as they change it. It also has many more developers and much more work done on it all the time.
It'll be a while before Apache's office catches up, and then it has to thrive and exceed the others. Which I don't really see happen.
You only have to load the two up side-by-side to see which one is actually a more "complete" and usable office suite, and just look at the code to see which has cleaner code. In one of the LibreOffice releases they deleted / translated some thousands of German comments and hundreds of unused functions, for instance. That suggests they had a much better understanding of the code and what it does and what is used before Apache OO even existed.
I think Libre has "won" and will probably continue to "win" for a while yet. Until then, the others are just free sources of patches.