For me, it's the opposite. Chrome's search bar does what I want predictably (run a Google search) where the awesome bar sends me all sorts of crazy places. It's that feature alone that keeps me on chrome.
I guess it depends on what you want to do. The Firefox awesome bar does a better job at guessing what bookmarked or historical site you want.
For instance, if I type in "y" or "yc" in Firefox, then it correctly guesses that I probably want "news.ycombinator.com", because it's a site I often visit and one of the very few with "y" or "yc" in the domain name.
Chrome, on the other hand, seems to only match from the start of bookmarked URLs. So "y" doesn't match, and nor does "yc". Instead it advises me to do a Google search. On the other hand, if I type "n", then it does guess that I want "news.ycombinator.com" (or "news.bbc.co.uk").
In Firefox 4, the default address bar search changed to a regular Google search, rather than the "browse by name" behavior used in Firefox 3.6 which would sometimes do a search and sometimes go straight to the top result [1]. It should be much more predictable now.
For me, it's the opposite. Chrome's search bar does what I want predictably (run a Google search) where the awesome bar sends me all sorts of crazy places. It's that feature alone that keeps me on chrome.