The major disadvantage that comes with hosted solutions is that you have no control over the service. Consider Yahoo Groups, which deleted all of its mailing list archives last year. I was one of the project leads for the Archive Team effort [1] to make a copy of those groups before they were lost forever, and although we saved several hundred thousand groups, we lost a lot more. Many millions of groups just vanished. Many of them, despite being long abandoned, were basically the only evidence left of that community, containing vital archives and information that is now gone.
I'm not saying this doesn't happen with self-hosted groups, but if a self-hosted group decides to shut down, it's their choice. (Rather than Yahoo emailing you to tell you that everything will be gone in a month).