LibreOffice and OpenOffice both use the OpenDocument format, and LibreOffice is based on OpenOffice. But how compatible are they which each other?
With regard to ODF support, there is substantial common code. In that respect, the coverage of the ODF feature sets are comparable. Improvements and fixes in this area will likely remain synchronized, as will any common security vulnerability repairs. Both projects have participants who are also on the OASIS ODF TC.
Other differences arise as the result of variations in features of the application and especially functions such as conversions to and from other formats, provision of authoring tools (spell checkers, etc.), internationalization, macros, Java dependencies and so on, features that are not subject to the ODF specification. Some of these differences result from the licensing change for Apache OpenOffice, and the restriction that Apache projects observe concerning code under incompatible licenses. Other differences (such as the absence of OOXML export in Apache OpenOffice) are more ideological in origin and will likely disappear over time.
Code sharing from Apache OpenOffice to LibreOffice is rather easy, so far, because the Apache license is completely open for that, and it is happening around features being adapted into Apache OpenOffice from Lotus Symphony user interface and accessibility support. It appears that the projects pay attention to each other's bug reports too.