While each Firefox release brings some new features, if you're looking to be the first, the Aurora releases and especially the Nightly ones are what you need, as long as you can put up with the bugs.
New features land in Firefox Nightly constantly, luckily Mozilla sometimes provides a roundup of the most recent additions.
Firefox now supports favicons with multiple images, meaning websites can serve two favicons, one for regular displays and one for HiDPI displays. That's great for users with high-resolution displays, though there aren't that many of them around.
Firefox is also getting performance improvements under the hood, to startup times, better scrolling on touch pads and smoother animations.
The new multithreaded image decoder is going to have the most importance. Images are still the biggest resource, at least in terms of size, on most sites. Especially with a lot of tabs open, the new decoder will make a noticeable difference.
Also under the hood, the most recent Firefox builds add support for a new HTML input type, "range." This provides a slider input, which can be used to retrieve a value from a specific range.
There's also support for HTML5 notifications, the most recent specs, the feature is now fully supported in Firefox. Chrome has already had support for the feature as Google is betting big on it, particularly for Google Now.
Another area where Firefox is finally on par with Chrome is the Web Audio API, which is now enabled by default.
CSS @supports is available in Firefox 22. As the name suggests, it allows developers to test whether features are supported in the browser to make it easier to target different browsers. It also makes it easier to work with prefixed features.
The CSS Flexbox is supported in Firefox again, though "min-width" and "min-height" can no longer be set to "auto."