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.

Thank you for respecting your user's privacy. This is one of the many reasons I use Firefox over Chrome.

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.

Can't you use regexp to differentiate urls from search terms and only send search terms?

How? Do you start all your URLs with "www"? I know I don't, so a regex couldn't possibly know until I typed either a space or a dot.

On the other hand, if you could make this work, I'd love to see it.

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.

In Opera typing g + space begins a Google search. The prefix is stripped off before it's sent.

Your alternative method is Chrome behaviour (of course it gives suggestions even if you don't prefix with ?, but the keyboard shortcuts are there)