Dropbox's idea of the cloud is file based. Apple's idea of the future of computing (iOS and iCloud) is no files, you just assume apps will use the cloud. It's clunky because it's not what we are used to, nor the app makers.
I'm not so sure their long term view of the cloud is necessarily "file based" (although it's debatable what that means specifically).
Dropbox was originally IIRC developed by a college student who had the problem of sharing files easily between his home and college computers, dropbox was a solution to that.
In the long term however , they have more or less solved the basic problem of syncing files and used this to provide revenue to move into the future.
I see a good business model for them could be to provide a platform for developers to build things that may in the background be syncing files (I think it'll be a while before we have filesystemless servers especially since unix is build around the concept of files) but from the end user point of view are providing services like photo / calender sharing etc.
