Há uma extensão do Chrome no navegador, DropboxDiff . Aqui está a descrição:
DropboxDiff offered by Victor Shih
Compare versions of your Dropbox files in-browser or with your configured diff tool. Trigger from any "Previous versions" page. Provides two options for comparing different versions of your Dropbox files: 1) a side-by-side diff within your browser, or 2) an external diff tool. This can be TortoiseMerge, kdiff3, FileMerge, or any tool which can be triggered from a command line.
In the "Previous versions" view of the Dropbox web interface of any file, a column is added which allows you to select two versions to compare. Click the Inline button to view the difference in-browser, or the Diff button to trigger your configured diff tool.
Supports Windows, Mac, and Linux as far as I know, though I can't be sure every possible configuration is covered.