I think the Chrome approach should be the default approach. By default the browser should aim to be appliance-like. As others have stated, most non-computer savvy folks struggle with exactly what a browser is, and how it differs from an operating system.
However, those who do want or need control should have it.
So I think the default behaviour of a browser should be Chrome style, but they should be configurable to use Firefox style behaviour, and also to allow centralised update control for enterprise environments.