I guess a big difference is that your data isn't stored at a 3rd party somewhere. That's one of the things that are good about Dropbox - if you delete your stuff, you can go back and fetch it.
It is also one of the things that are bad about Dropbox: even if you delete your files, someone else still has a copy. Worse, it's almost never encrypted client-side.
That is often not an issue of course, Dropbox is great.
Dropbox has its demons, however, and it's probably not something you should rely on for its security.
I used to use it as a means of keeping an encrypted file synced across machines, but when you re-lock up the file it... well, encrypts it, which means re-arranging ALL the bits, so a diff (how dropbox syncs) is just the whole damn file.
> I guess a big difference is that your data isn't stored at a 3rd party somewhere.
I think a word which could be missing here is "necessarily". I see no reason why you couldn't have "remote" sync devices provided by third parties, including but not limited to Dropbox. So if you want to store your data at a third party, you can. If you want a remote storage under your control, you can. If you don't want remote storage, you can.