What does Chrome's Omnibar do for you? It lets you type in URLs to websites like any other address bar, and it lets you search Google by typing in a search query instead of a URL. Oh and when you're typing the URL to a page you frequently visit, it auto-completes it for you. Is that all?
Well, Firefox's AwesomeBar (their word for the same feature) does all of the above just as well, and then some. Want to search Google? Just type in your search query. It all works exactly the same way as Chrome. Firefox has been doing this before Chrome even existed. Auto-completing URLs? Firefox does this too.
But then Firefox goes way beyond. You saw a post on Reddit 5 months ago, and you know it's somewhere in your history and you wanna find it? Just type one or two words that appeared in the page title. Firefox's AwesomeBar will show suggested results as you type based not only on the URLs, but also on the page titles. Bam. You can find any page in your history just by typing a word from the title. With Chrome, the only way to find an old page is to begin typing its URL out. This requires you to know a lot more about the link than you need to know for Firefox.
For a Reddit example, say you want to look up a post you saw recently about the Galaxy Nexus Android phone. Was it posted to /r/android? Or was it /r/technology? Maybe it even was mentioned on /r/apple? You don't remember, you just remember the post was about the Galaxy Nexus. Just type "galaxy" in your AwesomeBar and you'll probably find the link in 2 seconds or less. With Chrome, you'd have to begin typing out, "reddit.com/r/android" and try all the various subreddits that it might have been posted to. You're better off opening the history window and searching for it. There's just no easy way.
Firefox 1, Chrome 0.