Matching version numbers shouldn't make a difference, it is when calibre starts that things get affected.
The same problems that don't happen when you upgrade on one computer, won't happen when you transfer to a computer with a newer version.
calibre will upgrade the database schema if necessary -- which it usually isn't. But it cannot hurt to avoid moving to a computer with an older version installed.
And I have seen someone somewhere claiming that they have had no problems migrating the config folder between OSes (except for the changing library locations which is an easy fix). Take that with a grain of salt of course.
