I think Chrome is able to do this because it separates tabs into processes, but I don't think there's a good way for Firefox to do it since everything is in a single process.
I think the problem with that is it doesn't work with Flash audio. With multiprocess browsers, the Flash audio can be associated with a tab, but that's awkward/not possible if everything is in the same process.
Chrome didn't have this feature for a very long time, and if anything sounded like it was actually harder because of how Chrome handles their processes.
Well, Chrome still often shares the same process for groups of tabs. I think this particular feature has something more to do with a change they made to their plugin API.
https://bugzilla.mozilla.org/show_bug.cgi?id=486262