Why not both ways? And, why not a device security service?
There are merits for the "mainframe" approach to just connect to and not fill a local file system (thinking on tablet, phone scenario). With trouble you can save files on your local device. Why not selective sychronization?
Apple would probably have to iRedesign to provide a cloud app service, but then would have to offer it for free and where would that put iTunes/store?
One glaring security feature for the Apple/local device model is data destruction on the local device. Why not have a mechanism for being able to trigger a data scrape on a lost device?
Or how about file support for non-Apple data or non-Apple apps? Having MAC, droid, Linux, Windows in our family makes the Apple solution quite unattractive as a backup repository service. A non-OSX client would be easy enough for backup/synchronization of data files.