No, not at all.

Web apps automatically update, and you basically don't run any code on your machine. Whoever is running the webapp can usually see everything you do. Google knows you opened and edited that document at 4am last Thursday. If someone serves Google a warrant, they'll give them your documents. You also don't have to trust whoever is running the webapp. You can use Joe Shmoe's interactive Diablo map and the only risk is the data you give them.

Desktop apps may or may not phone home. But generally if you edit a document in notepad or WordPad, nobody has that information but you. If someone wants that document, they need to get access to your machine. But it does require you to run code that you can never really be sure of what it's doing. So you generally want to stick to known names or people you can trust. Don't run random executables on your machine. Note that this is also why it's so much harder to pirate games or software than it is to pirate media. You (generally) can't get a virus from an mp3 or mpeg or jpeg file.