I've had a look at Google's docs[1], and it's really not clear to me what Chrome's omnibox offers that Firefox's address bar (or whatever they call it) doesn't.
I've got Aurora installed for Tor and flash-based apps that don't play nicely with Chrome, but I still use Chrome for my daily surfing and so have not really noticed any of the changes Mozilla has made. If the address bar really is reproducing the functionality of the omnibox, why not kill the search box all together? It seems like duplicated functionality and a waste of screen real estate.
I think the only use for the search box now is to give people easy access to multiple (or a secondary) search engine. Sure, it's ugly, but it does give users a clear and simple way to search wikipedia for "widgets".
Chrome, on the other hand, only exposes non-Google search engines through the search engine keyword thingy, which means a user has to actually type "en.wikipedia.org widgets" into the omnibox. Sure, tab-completion will do half the work, but the user still has to remember to start typing "en." rather than, say, "wikipedia".
I know that Chrome (and, indeed, Firefox) allow you to edit those search engine keywords, but that is power-user territory, and power-users can edit their Firefox UI as well. http://i.imgur.com/mS5Ot.png
Minor quibble, but Chrome makes it pretty easy to change your default search engine to anything you want, including non-Google search engines. It's not that you need to use a keyword to search a non-Google search engine, it's that you need to use a keyword to search a non-default search engine. :)
Also, the UI in Firefox for changing the address bar search engine is awful -- about:config, click through the warning, then find and edit keyword.URL (which is in a different format to everything else)
Some of us actually like distinguishing between URLs/bookmarks/history and an autocomplete-with-search-engine-spying search facility. I don't view the trend of combining them into a single text box as a positive one, whichever browser is doing it.
