An advantage you have is people who are already invested in your site. If they have a good ranking going or some friends on the site they won't be very interested in packing up and going elsewhere. You could try and make the site as viral as possible (wall integration, send to a friend, etc) to try and snowball your users into more users.
You can try to direct some of that attention to yourself, since you're in the same space. You can't compete on prizes, but you'll have a different offering - you have to distinguish your product from Yahoo's product in other ways.
