Compare the text contents by saving as plain text in both versions and then compare the plaintext version.
Or use Word Count from Tools|Options of from the Document statistics.
Or use the compare documents functionality (Edit|Compare documents) on copies of your files.
Other than that - what order of magnitude is the change in filesize? It could be that a preview thumbnail is not created on linux while it is on windows for example.
Also different setting of “optimize ODF document for size” in Tools|Options→Load/Save→General can have a small impact (when not optimizing for size, the xml will have linebreaks and indentation, while when optimized for size, it is all stuffed in one single long line)