Whether the noisy tab indicator will actually make it to the mainstream version of Firefox is unclear. But I was able to grab an early test build of Firefox to see how the feature is developing.
Hands-on with Firefox's very early mute noisy tabs feature
Similar to Chrome's implementation, Firefox's early trials display a noise indicator in your browser tab. If you want to mute the audio, you hover over the noise indicator, right-click it and select Mute Tab. Boom! No more noise. The mute feature also works even if the noisy tab isn't the active page.
In the test build that I tried, this very early feature only works with HTML5-based videos and not Flash. However, developers appear to be working on implementing the ability to detect Flash audio as well.
As the feature stands right now it feels like a bit of a cheat. In my tests, the browser simply pauses the video when you hit the Mute Tab option. Oddly, the video pause is independent of the actual video player controls on the tab itself.
In other words, if you try to play/pause the video with the usual player controls after you've hit the mute tab control, the video won't start. To get the video going again you'll have to unmute it first via the tab's noise indicator.
It's clear this feature isn't ready for prime time yet--but that's to be expected as the feature is only in the very early test phases. The important thing is simply that it's being worked on.
The impact on you at home: It's not clear when it might land in the stable version of Firefox. At this writing it wasn't even available in the official nightly builds. However, considering how many people love this feature in Chrome, my guess is it's highly likely the mute tab feature will become a standard version of Firefox--as long as the development process doesn't hit any major roadblocks.
The Flash feature crash
While the mute tab feature is still in early days on Chrome as well, the actual noise indicator itself is more than a year old. Google was able to beat other browsers to the punch with this feature, because its noise indicator works with both HTML5- and Flash-based media.
Google has a customized version of the Flash Player built-in to Chrome, which presumably means it can develop features for Flash that other browser makers can't. Until recently, the standard version of Flash did not offer a way for browsers to figure out if a sound was playing from Flash-based media. All Firefox could do was know whether Flash was in use at all.
That's doesn't help much since it would be silly and confusing to put a noise indicator at the top of a tab if, say, Flash was only being used to display a silent animated ad. It also isn't great for the user to only have a tab noise indicator when HTML5 videos are playing--unless, of course, you knowingly wanted that feature by installing the Noise Control add-on.
So Firefox developers were stuck with a Flash problem until earlier this year when Adobe added the ability to detect Flash-based audio. That said, it's entirely possible Mozilla could release this feature with the HTML5 functionality first and then add Flash compatibility later.
Regardless, let's hope we see this feature hit Firefox very soon. I can think of a few sites this would be useful for, and I'm sure you can too.