Dropbox is mixed web and desktop, as a large part of its functionality is exposed (only) through the web interface. Its desktop parts are probably born more out of necessity than desire: a web app simply cannot "sync a folder".
I have never once used Dropbox's web interface (I haven't even bothered to look at it). What part of the functionality is missing from the desktop application? The only functionality I need or use is dropping files into the Dropbox folder and knowing they're not going to be destroyed if a hard drive fails or the house burns down.
restoring a deleted file and versioning comes to mind, if i am not mistaken?
To my knowledge, sharing folders can only be done through the Web interface.
'Events', a list of creations, changes and deletions.