I think pinboard is a great example of competing with a free product (delicious). Pinboard has focused exclusively on a core set of features, with a particular focus on being the minimal bookmarking web app. This page they created does a good job of comparing them to their competition http://pinboard.in/switch/ .

I mention all of this to say that I would focus on what exactly makes your app better. The goal may not be to win against the free app, but to make the best app you can while focusing on the paying users.