I would say that the latter is far more severe. People are going to be a lot more complacent when they believe that the data they are storing can't be accessed by others, or is otherwise immune to attacks. There's also the distinct possibility that the user is going to be storing sensitive information that they wouldn't normally store anywhere but locally.
Don't get me wrong, I love encryption, I just get uneasy around browser implementations. There's some very fragile ones in use at the moment (see mega.co.nz, blockchain.info).