Advantages: The entire repository is a single file (SQLite database), which makes some things easy (backup, putting it on a USB drive, mailing it to another person) and has support for tickets and a wiki built-in. It is simple, but feature-complete for the use cases it is intended for.
Disadvantages: The command line interface is lacking in some regards (which can be fixed through addon tools, but isn't for everybody). In particular, there's a huge feature gap between `fossil ui` and `fossil timeline` for viewing history. Like Git (and unlike Mercurial and Bzr), you're forced to deal with commit hashes rather than numerical version numbers (which can be an annoyance when using annotate/blame, for example). Third-party contribution via `fossil bundle` is too limited IMO; you really want all contributors to have direct access to the repository to be productive.