Elephant in the room is the ugly and unnecessary search box. It sticks out like a sore thumb when you consider the effort Firefox has gone through to clean up the interface.
side rant: what's up with search boxes that keep your previous search term in the box. What's the point? iPad does this as well and it drives me insane. I always just manually delete the entry after searching but I shouldn't have to do that and I don't want guests to know my previous search.
You can of course customize the toolbars [1] to remove the search bar, since you can also search through the address bar. But unlike the search bar, the address bar does not show suggestions as you type, because of the privacy implications of sending everything you type there to a third party. (There are add-ons to change that if you want to.)
The search box provides suggestions, but it does this by sending everything you type to your search provider. The address box doesn't, because we feel it's bad for privacy to send every web address you type to a third party.
FWIW, it's an option in Chrome. Simply uncheck "Use a prediction service to help complete searches and URLs typed in the address bar" in the preferences.
But with Firefox, your search box can still make suggestions while not sending web addresses to a third-party, thereby allowing you to have your cake and eat it too.
Perhaps we could do the reverse? Provide search suggestions if the user explicitly tells us to by beginning their input with a special character. '?' perhaps.
Alternatively, although not intuitive, if the user enters focus with the search bar through a specific key-stroke: CTRL + L for a regular URL entry, and re-route CTRL + K to our web-bar, but with suggestions.
I like the search box because the URL history autocomplete of the main URL bar is so much better in Firefox than any browser. I can type any part of a page title or URL (not just the start) and it goes through and finds pages from my history. I do that much more often than I search for things and so I really like having them separate.
Whenever I switch to another browser (such as IE at work because it is mandated for 'security reasons') that is the first thing I miss. In many cases I only type one letter before getting what I want.
Chrome searches your history and offers the search option, without requiring a separate search box. It doesn't force you to use the start of the URL or title, either, as far as I can tell.
The chrome address bar search tokenization seems much more simplistic. Something like splitting on path elements would help me match "finance" when searching through my history for google.com/finance
Everything you type in Chrome's single address bar is sent to Google servers. In Firefox, only the stuff you type in the search bar reaches servers for auto-completion, but the location bar is entirely local.
This is an important distinction for privacy, but you are right that we may need to come up with a better UI that unifies the two boxes whilst maintaining the distinction between a local and remote search. The "prospector" series of experimental add-ons from Mozilla Labs have some ideas in this area, most notably AwesomeBar HD: https://mozillalabs.com/prospector/2011/04/27/awesomebar-hd-...
The "search bar keeping your previous search term" issue has to do with the ownership of the search box. It used to be, when tabs were below the search box, that made sense. You'd be using the same one search box no matter which tab you were on, and thus it would always keep the same search term between tabs.
Now, with tabs-on-top, each tab contains its own search box. These should be unique, just like each tab has its own URL bar. It doesn't make sense at all that search queries are preserved between tabs. But that's the way Firefox still does it.
(Thinking about this now, I guess that's a different issue than the one you were talking about... why any search box saves any query after pressing "Enter". Still an annoying little quirk though.)
I am not sure about FF5, but on FF4 though the search bar kinda seems to be related to the particular tab, it is still the common search bar and the things I searched while at one tab are displayed in every other tab. I am using Ubuntu 11.04/Firefox 4.0.1
At least when you click from tab to tab the URL bar changes, that's the important part if you're faking it. The search bar keeps the same query on every tab.
And the saving the search term thing is that way because that's how Google-the-website works. Search for something on google.com, and the Results Page shows that term in the box. The Search Box behavior was just carried over from that.
If you use more than one search engine, keeping the term after pressing enter can make a lot of sense.
Example: If I search wikipedia and that produces no results, I'll google the same term instead.
That said, it would probably make sense for it to clear out after a few minutes, or after your interaction seems to indicate that you're done with that search term.
Not the intended purpose, but the search box has been very useful to me in the past as a quick second paste-buffer, much quicker than opening a text editor or anything to place it in.
It might not be necessary, but it is the one feature I prefer about Firefox than Chrome. I use it a lot and it is more handy to change search engines or to search other sites than typing those things in my hand in Chrome.
side rant: what's up with search boxes that keep your previous search term in the box. What's the point? iPad does this as well and it drives me insane. I always just manually delete the entry after searching but I shouldn't have to do that and I don't want guests to know my previous search.