Where is your competitor based? Which jurisdictions are valid wrt copyright infringement? How do you know they haven't applied for rights (eg via a clearing house)?
Note that there are still some places in the world that are not signed up to Berne/TRIPS and the like international treaties. A person (or presumably a web server) based there who (on which) compiles such would be untouchable on copyright infringement. Moreover, many places allow excerpts/snippets to be used and the definition of "commercial use" varies around the world.
I suspect all you can really do is improve your content or put money before morality.
>I suppose you can make a few hundred a month in advertising
A few hundred what? US Dollars, GBP, Euro, ... why is this important to you?