The problem of keeping things secret and doing a big hype launch is that you don't get any customer feedback. Apple can get away with that because the Apple-lovers will ignore most problems in exchange for the beautiful UI.
I don't recommend secrecy for startups. Getting your product to the user's hands as early as possible should be your #1 goal. Yeah, a big company might steal your idea, but they won't because they are too big to pay attention at small companies. Plus, they are a big company so they think they are better, thus, your idea has to be inferior. Luck you.