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
