If the app is free software it can be audited. The problem with web-based crypto is that you're downloading a new program every page refresh and executing it immediately. If you're worried about a free software app not encrypting things properly, I'd be worried about the tools you use manually doing the right thing as well.

While I agree that doing it manually is the only reliable way if you're going to send it over an insecure channel, if the channel is secure then it's much easier for an end-user to just send it in the app.

And that's still just a feeling. You just feel you can trust the encryption application. Which can be changed any time in the future in a way it is not secure any more.

You just need to trust. So what's wrong in trusting Mozilla, if you can easily trust your encryption/decryption software?

Why would you trust 7-zip or NotePad++ more than FireFox?