Running an application written in Javascript in my browser is more convenient and surely no more dangerous than installing and running an application written in C/C++/Java/whatever directly on my computer?
In total, it would be more dangerous. If you have an audited application to handle a particular type of data, then downloading countless unaudited applications from unknown sources is less secure.
Not enough, and worse, auditing is never a guarantee.
None the less, at least the perceived risks of audited code seem to be less than unaudited code, and there is at least some data to support the assertion. It's not a guarantee of perfection, but it does seem better than the alternative.