Why not offer both? Casual users might prefer to use the web app, advanced users can mine their own data. However, if I were to use a plugin to export my search data, I would expect it to be good at capturing/extracting search queries on a variety of websites and maybe have some additional features. Otherwise, I could just mine my Firefox history directly.

By the way, you could build a web app that runs on the desktop with Appcelarator's Titanium, or port the existing one to Titanium.