I love agent-judged contests. For querying writers, they're a great way to grab an agent's attention. It's almost like bypassing the slush pile because it's an observable fact that many agents give more time and attention to contest submissions. Participants get the benefit of direct agent feedback, but the information is useful for all writers.
It's a learning experience to read through real examples of what pings an agent or what turns them off, what we should do more of and what an agent might be tired of seeing. Keeping in mind, of course, that responses might be particular to that specific agent, especially concerning taste.
For me, it's fun to see what other writers are working on. But I also like to read through the submissions and compare my response with others, including the agent's reaction. It's interesting to see how opinions vary, and whose opinions fall in line with mine.
When I was still querying, I liked to find contests a particular agent judged and read through her/his responses. It was a great way to gauge how they might receive my query.
Krista over at Mother. Write. (Repeat.) has this awesome post about Why You Should Enter Blog Contests. I agree with everything she says :)