Absolute links are easier but if you ever move a site they can cause trouble. This is an absolute link:
It doesn't matter which page you put that link on (or which site) it will always point to the same place. Relative links will work or not work depending on where you put them.
If all the pages on this site were linked to each other with absolute links and I then moved the site to another server the links would no longer work. It is best to only use absolute links for links to other sites.