/Insert grumblings about insecurity of the omnibox (leaking internal corporate data) and my personal preference for firefox-style URL box and search box.
Also, I find the firefox awesome bar much more powerful than Chrome's it does (fuzzy?) word search on every url and title in the history, and here always seem to give me more pertinent results than Chrome's (which seems to forget I visited a website in just a few days).
I've found this exact same thing as well - the FF awesome bar always seems to give me the results I want, whereas I have to do a lot more specific and manual typing to find what I want in the Chrome bar. This could be an interesting blog post I'd think: comparing the implementations of the matching algorithms of Chrome vs. FF vs. possible others.
You can get search suggestions in the Awesome bar (URL bar), but it asks you before it gets turned on.
(I personally always the Firefox search bar, but I also decline the search suggestions because they don't help me much. Instead I have 15–20 keyboard searches I use a lot.)