The difference is following:
Update to HEAD will do svn update.
In other words it will update your working copy to the last revision from the repository.
Synchronize with Repository is something similar to svn status -u, but even more.
It will open a Synchronize tab (or perspective) that displays overview of your local (outgoing) modifications versus repository (incoming) modifications.
In this tab or perspective, you can review and synchronize (commit / update) individual files, see differences between your working copy files and incoming files from repository, browse commits history, resolve conflicts.
In general, I highly recommend you to check out the SVN Handbook.
At least first two chapters.