You keep the data fully under your control. Who knows whatever ram-scanning-key-searching tricks Dropbox or any other Closd Source piece of software utilize...
Does dropbox run as root?
You install the package/setup as root.
You don't have to, if you want to be that paranoid.
Why would dropbox even need that level of obfuscation for a backdoor? The binary just do evil directly (although having something that seems plausibly like a bug would be ideal.)
Big issue for me re: Dropbox clones, device integration/clients. iOS being key for me.